A341056 a(n) = n! * [x^n] exp(x/(1 - n*x)) / (1 - x).

1, 2, 9, 106, 2801, 132426, 9705577, 1015001954, 143392421601, 26298332570386, 6074043257989001, 1724846814877790682, 590605908915568818769, 239956225437223244619866, 114123836188192016600789481, 62808518765936960824453590226, 39603421893790601518269204039617

Offset

0,2

Links

Table of n, a(n) for n=0..16.

Formula

a(n) = n! * Sum_{k=0..n} A341033(k,n)/k! = n! * (1 + Sum_{j=1.. n} Sum_{k=1.. j} n^(j-k) * binomial(j-1,k-1)/k!).

a(n) ~ BesselI(1,2) * n! * n^(n-1). - Vaclav Kotesovec, Feb 14 2021

Example

a(3) = 3! * (1 + 1/1! + 7/2! + 73/3!) = 106.

Mathematica

Table[n!*(1 + Sum[Sum[n^(j-k)*Binomial[j-1, k-1]/k!, {k, 1, j}], {j, 1, n}]), {n, 0, 20}] (* Vaclav Kotesovec, Feb 14 2021 *)

Prog

(PARI) {a(n) = n!*(1+sum(j=1, n, sum(k=1, j, n^(j-k)*binomial(j-1, k-1)/k!)))}

Crossrefs

Cf. A277373, A293146, A330260, A331658, A341033.

Sequence in context: A132494 A136172 A012986 * A309452 A354663 A219116

Adjacent sequences: A341053 A341054 A341055 * A341057 A341058 A341059

Keyword

nonn

Author

Seiichi Manyama, Feb 04 2021

Status

approved