A371430 - OEIS

A371430

Expansion of (1/x) * Series_Reversion( x / ((1+x)^4 - x^2) ).

1, 4, 21, 128, 851, 5984, 43759, 329396, 2535406, 19863592, 157874971, 1269833668, 10316765299, 84540929568, 697928139977, 5799156785376, 48461097907978, 407020852551016, 3434002483872566, 29090171931564848, 247333930963224287, 2109921586071433064

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OFFSET

0,2

LINKS

Robert Israel, Table of n, a(n) for n = 0..1039

Index entries for reversions of series

FORMULA

a(n) = (1/(n+1)) * Sum_{k=0..floor(n/2)} (-1)^k * binomial(n+1,k) * binomial(4*n-4*k+4,n-2*k).

D-finite with recurrence: (-24960*n^3 - 149760*n^2 - 274560*n - 149760)*a(n) + (105344*n^3 + 862080*n^2 + 2308864*n + 2012160)*a(n + 1) + (-188000*n^3 - 1984800*n^2 - 6981568*n - 8157504)*a(n + 2) + (176912*n^3 + 2326176*n^2 + 10216480*n + 14972256)*a(n + 3) + (-92104*n^3 - 1455168*n^2 - 7666256*n - 13465872)*a(n + 4) + (23740*n^3 + 433140*n^2 + 2630696*n + 5318472)*a(n + 5) + (-1948*n^3 - 39780*n^2 - 270056*n - 609360)*a(n + 6) + (27*n^3 + 648*n^2 + 5181*n + 13800)*a(n + 7) = 0. - Robert Israel, Mar 11 2026

MAPLE

f:= gfun:-rectoproc({(-24960*n^3 - 149760*n^2 - 274560*n - 149760)*a(n) + (105344*n^3 + 862080*n^2 + 2308864*n + 2012160)*a(n + 1) + (-188000*n^3 - 1984800*n^2 - 6981568*n - 8157504)*a(n + 2) + (176912*n^3 + 2326176*n^2 + 10216480*n + 14972256)*a(n + 3) + (-92104*n^3 - 1455168*n^2 - 7666256*n - 13465872)*a(n + 4) + (23740*n^3 + 433140*n^2 + 2630696*n + 5318472)*a(n + 5) + (-1948*n^3 - 39780*n^2 - 270056*n - 609360)*a(n + 6) + (27*n^3 + 648*n^2 + 5181*n + 13800)*a(n + 7), a(0) = 1, a(1) = 4, a(2) = 21, a(3) = 128, a(4) = 851, a(5) = 5984, a(6) = 43759}, a(n), remember):

map(f, [$0..30]); # Robert Israel, Mar 11 2026

PROG

(PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x/((1+x)^4-x^2))/x)

(PARI) a(n) = sum(k=0, n\2, (-1)^k*binomial(n+1, k)*binomial(4*n-4*k+4, n-2*k))/(n+1);

CROSSREFS

Cf. A317133, A369156.

Cf. A369213.

Sequence in context: A099250 A293192 A300674 * A232956 A390811 A234268

Adjacent sequences: A371427 A371428 A371429 * A371431 A371432 A371433

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Mar 23 2024

STATUS

approved