A259859 a(0)=0; thereafter A003470(n-1) + A003470(n) - 1.

0, 1, 3, 10, 38, 177, 999, 6676, 51564, 451585, 4418555, 47746686, 564528978, 7247396065, 100378220943, 1491699317032, 23673159231704, 399553959924801, 7146023007880179, 134997604341408370, 2686037319660797310, 56143557248353416721, 1229914413684635491703

Offset: 0

Author

N. J. A. Sloane, Jul 07 2015, based on a suggestion from John Riordan, Nov 14 1974

Keywords

• nonn

Links

• John Riordan and N. J. A. Sloane, Correspondence, 1974

Crossrefs

Cf. A003470.

Programs

Maple

b:= proc(n) b(n):= `if`(n<2, 1, n*b(n-1)-b(n-2)+1+(-1)^n) end:
a:= n-> `if`(n=0, 0, b(n-1)+b(n)-1):
seq(a(n), n=0..22);  # Alois P. Heinz, Jun 17 2021

Mathematica

b[n_] := b[n] = If[n<2, 1, n*b[n-1] - b[n-2] + 1 + (-1)^n];
a[n_] := If[n == 0, 0, b[n-1] + b[n] - 1];
Table[a[n], {n, 0, 22}] (* Jean-François Alcover, Dec 26 2022, after Alois P. Heinz *)

Formula

D-finite with recurrence: (-n+2)*a(n) +(n-1)^2*a(n-1) +2*(-n+2)*a(n-2) +(-n^2+4*n-2)*a(n-3) +(n-1)*a(n-4)=0. - R. J. Mathar, Jul 15 2015

Extensions

Offset corrected by N. J. A. Sloane, Jun 16 2021