A344496 a(0)=0; for n > 0, a(n) = a(n-1)*n + n if n is odd, (a(n-1) + n)*n otherwise.

0, 1, 6, 21, 100, 505, 3066, 21469, 171816, 1546353, 15463630, 170099941, 2041199436, 26535592681, 371498297730, 5572474465965, 89159591455696, 1515713054746849, 27282834985443606, 518373864723428533, 10367477294468571060, 217717023183839992281, 4789774510044479830666

Offset

0,3

Links

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

Formula

a(n) ~ n! * (3*exp(1)/2 + exp(-1)/2). - Vaclav Kotesovec, Jun 05 2021

Example

a(0) = 0;
a(1) =  a(0)*1 + 1 =   0 + 1    =   1;
a(2) = (a(1)+2)* 2 =  (1 + 2)*2 =   6;
a(3) =  a(2)*3 + 3 = 6*3 + 3    =  21;
a(4) = (a(3)+4)* 4 = (21 + 4)*4 = 100.

Maple

a:= proc(n) a(n):= n*a(n-1) + n^(2-(n mod 2)) end: a(0):= 0:
seq(a(n), n=0..22);  # Alois P. Heinz, May 21 2021

Mathematica

a[0] = 0; a[n_] := a[n] = n * (a[n - 1] + If[OddQ[n], 1, n]); Array[a, 30, 0] (* Amiram Eldar, May 21 2021 *)
Table[n*(-1 + 3*E*Gamma[n, 1] + (n-1)*Subfactorial[n-2])/2, {n, 0, 30}] (* Vaclav Kotesovec, Jun 05 2021 *)

Crossrefs

Cf. A344262, A344495.

Sequence in context: A009247 A093774 A151612 * A012773 A012662 A012418

Adjacent sequences: A344493 A344494 A344495 * A344497 A344498 A344499

Keyword

nonn

Author

Amrit Awasthi, May 21 2021

Status

approved