A352430 a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/5)} binomial(n,5*k+1) * a(n-5*k-1).

1, 1, 2, 6, 24, 120, 721, 5054, 40488, 364896, 3654000, 40249441, 483659508, 6296246424, 88269037584, 1325861901000, 21243052172161, 361630022931666, 6518319228715302, 124018898163736536, 2483799332459535000, 52231733840672804881, 1150683180739820615582, 26502219276887376327696

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..449

Formula

E.g.f.: 1 / (1 - Sum_{k>=0} x^(5*k+1) / (5*k+1)!).

Mathematica

a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, 5 k + 1] a[n - 5 k - 1], {k, 0, Floor[(n - 1)/5]}]; Table[a[n], {n, 0, 23}]
nmax = 23; CoefficientList[Series[1/(1 - Sum[x^(5 k + 1)/(5 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\5, x^(5*k+1)/(5*k+1)!)))) \\ Seiichi Manyama, Mar 23 2022

Crossrefs

Cf. A000670, A006154, A243666, A333882, A352428, A352429.

Sequence in context: A114796 A265086 A114790 * A292749 A351984 A365977

Adjacent sequences: A352427 A352428 A352429 * A352431 A352432 A352433

Keyword

nonn

Author

Ilya Gutkovskiy, Mar 16 2022

Status

approved