|
| |
|
|
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
|
|
|
|
0, 1, 6, 21, 100, 505, 3066, 21469, 171816, 1546353, 15463630, 170099941, 2041199436, 26535592681, 371498297730, 5572474465965, 89159591455696, 1515713054746849, 27282834985443606, 518373864723428533, 10367477294468571060, 217717023183839992281, 4789774510044479830666
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
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
|
| |
|
|
