A352428 a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/3)} binomial(n,3*k+1) * a(n-3*k-1).

1, 1, 2, 6, 25, 130, 810, 5881, 48806, 455706, 4727881, 53955682, 671730246, 9059714665, 131588822822, 2047796305470, 33992509701721, 599526848094850, 11195864285933682, 220692569175568729, 4579248276057441926, 99767702172338210898, 2277136869014579978473, 54336724559407913237122

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..447

Formula

E.g.f.: 1 / (1 - Sum_{k>=0} x^(3*k+1) / (3*k+1)!).

Mathematica

a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, 3 k + 1] a[n - 3 k - 1], {k, 0, Floor[(n - 1)/3]}]; Table[a[n], {n, 0, 23}]
nmax = 23; CoefficientList[Series[1/(1 - Sum[x^(3 k + 1)/(3 k + 1)!, {k, 0, nmax}]), {x, 0, nmax}], x] Range[0, nmax]!

Prog

(PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(1/(1-sum(k=0, N\3, x^(3*k+1)/(3*k+1)!)))) \\ Seiichi Manyama, Mar 23 2022

Crossrefs

Cf. A000670, A006154, A243664, A291973, A333881, A352429, A352430.

Sequence in context: A299044 A100325 A353180 * A352436 A020112 A317022

Adjacent sequences: A352425 A352426 A352427 * A352429 A352430 A352431

Keyword

nonn

Author

Ilya Gutkovskiy, Mar 16 2022

Status

approved