A367016 - OEIS

A367016

G.f. satisfies A(x) = 1 + x*A(x)^4*(1 - x).

1, 1, 3, 14, 78, 475, 3057, 20446, 140702, 989789, 7085635, 51451482, 378049810, 2805616460, 20999408480, 158337719608, 1201585477436, 9170328295222, 70339328959266, 541953619822062, 4192560258116202, 32552250308843605, 253583917423039079

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OFFSET

0,3

LINKS

Table of n, a(n) for n=0..22.

FORMULA

a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(k,n-k) * A002293(k).

D-finite with recurrence 3*n*(3*n-1)*(3*n+1)*a(n) +(-418*n^3 +951*n^2 -773*n+216)*a(n-1) +(2143*n^3 -10797*n^2 +18398*n-10512)*a(n-2) +2*(-2594*n^3 +20163*n^2 -52903*n +46800)*a(n-3) +4*(1627*n^3 -16836*n^2 +58532*n -68400)*a(n-4) -128*(2*n-9)*(16*n^2-132*n+275)*a(n-5) +256*(n-5)*(2*n-9)*(2*n-11)*a(n-6)=0. - R. J. Mathar, Mar 02 2026

PROG

(PARI) a(n) = sum(k=0, n, (-1)^(n-k)*binomial(k, n-k)*binomial(4*k, k)/(3*k+1));

CROSSREFS

Cf. A200753, A367017.

Cf. A002293, A365178.

Sequence in context: A330518 A228656 A244507 * A074538 A364739 A366083

Adjacent sequences: A367013 A367014 A367015 * A367017 A367018 A367019

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Nov 01 2023

STATUS

approved