A353262 Expansion of Sum_{k>=0} x^(2*k)/Product_{j=1..k} (1 - 3 * j * x).

1, 0, 1, 3, 10, 36, 145, 666, 3466, 19956, 124111, 821601, 5755987, 42634089, 333827776, 2759262897, 24000288202, 218806121205, 2082848200057, 20639203885008, 212441617055458, 2268057343273491, 25085332185250564, 287096974919978292, 3395697093278589844

Offset: 0

Author

Seiichi Manyama, Apr 09 2022

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..549

Crossrefs

Cf. A119429, A171367.

Cf. A353256.

Programs

Mathematica

a[n_] := Sum[3^(n-2*k) * StirlingS2[n - k, k], {k, 0, Floor[n/2]}]; Array[a, 25, 0] (* Amiram Eldar, Apr 09 2022 *)

PARI

my(N=40, x='x+O('x^N)); Vec(sum(k=0, N, x^(2*k)/prod(j=1, k, 1-3*j*x)))

PARI

a(n) = sum(k=0, n\2, 3^(n-2*k)*stirling(n-k, k, 2));

Formula

a(n) = Sum_{k=0..floor(n/2)} 3^(n-2*k) * Stirling2(n-k,k).