A365692 - OEIS

A365692

G.f. A(x) satisfies A(x) = 1 + x*A(x) / (1 - x^2*A(x)^4).

1, 1, 1, 2, 7, 23, 72, 238, 831, 2959, 10645, 38824, 143492, 535700, 2016020, 7641574, 29152015, 111841263, 431209723, 1669945778, 6493144143, 25338440143, 99204579648, 389570145288, 1534026813892, 6055885764548, 23962654178012, 95023123291680

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OFFSET

0,4

LINKS

Robert Israel, Table of n, a(n) for n = 0..1607

Robert Israel, Linear recurrence of order 16

FORMULA

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

D-finite with recurrence of order 16 (see link). - Robert Israel, May 18 2026

PROG

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

CROSSREFS

Cf. A101785, A365244, A365693.

Cf. A365690.

Sequence in context: A295136 A192906 A217664 * A083313 A064686 A077832

Adjacent sequences: A365689 A365690 A365691 * A365693 A365694 A365695

KEYWORD

nonn,changed

AUTHOR

Seiichi Manyama, Sep 16 2023

STATUS

approved