A385065 - OEIS

A385065

G.f. A(x) satisfies A(x) = 1 + x*(1+x^2)^2*A(x)^3.

1, 1, 3, 14, 67, 346, 1886, 10662, 61951, 367728, 2220254, 13593162, 84190978, 526573057, 3321150182, 21099247736, 134895625603, 867272099089, 5603614879376, 36367078947746, 236963815488922, 1549612756250929, 10166902568426922, 66904300124642096

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OFFSET

0,3

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

FORMULA

a(n) = Sum_{k=0..floor(n/2)} binomial(2*(n-2*k),k) * A001764(n-2*k).

MATHEMATICA

Table[Sum[Binomial[2*(n-2*k), k]*Binomial[3*(n-2*k), n-2*k]/(2*(n-2*k)+1), {k, 0, Floor[n/2]}], {n, 0, 25}] (* Vincenzo Librandi, Nov 16 2025 *)

PROG

(PARI) a(n) = sum(k=0, n\2, binomial(2*(n-2*k), k)*binomial(3*(n-2*k), n-2*k)/(2*(n-2*k)+1));

(Magma) [&+[Binomial(2*(n-2*k), k)*Binomial(3*(n-2*k), n-2*k)/(2*(n-2*k)+1): k in [0..Floor(n/2)]] : n in [0..30] ]; // Vincenzo Librandi, Nov 16 2025

CROSSREFS

Cf. A367059, A385317.

Cf. A366221, A389890.

Cf. A001764.

Sequence in context: A345683 A002320 A151323 * A389284 A354503 A181662

Adjacent sequences: A385062 A385063 A385064 * A385066 A385067 A385068

KEYWORD

nonn,easy

AUTHOR

Seiichi Manyama, Oct 18 2025

STATUS

approved