A375632 Expansion of e.g.f. exp(2*x) / (1 - x^3/6 * exp(x)).

1, 2, 4, 9, 28, 122, 624, 3523, 22824, 170948, 1422664, 12856373, 126598036, 1358773886, 15721899652, 194356158823, 2560950546576, 35899907132872, 533099244285136, 8351271711094697, 137675784924101596, 2383758487476054242, 43244905386257120044

Offset

0,2

Links

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

Formula

a(n) = n! * Sum_{k=0..floor(n/3)} (k+2)^(n-3*k)/(6^k*(n-3*k)!).

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(2*x)/(1-x^3/6*exp(x))))
(PARI) a(n) = n!*sum(k=0, n\3, (k+2)^(n-3*k)/(6^k*(n-3*k)!));

Crossrefs

Cf. A368265, A375631.

Sequence in context: A296264 A343166 A219665 * A241404 A005095 A300491

Adjacent sequences: A375629 A375630 A375631 * A375633 A375634 A375635

Keyword

nonn

Author

Seiichi Manyama, Aug 22 2024

Status

approved