A245176 a(n) = 2*a(n-1)+(n-2)*a(n-2)-(n-1)*a(n-3) with initial terms (1,2,4).

1, 2, 4, 8, 18, 44, 120, 352, 1116, 3736, 13232, 48928, 189080, 757584, 3148064, 13497600, 59704336, 271503648, 1268817472, 6078518912, 29837183008, 149789875904, 768674514816, 4026518397440, 21518708975040, 117199152735616, 650184360936192, 3670861106911744

Offset: 0

Author

N. J. A. Sloane, Jul 19 2014

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..800
• Tewodros Amdeberhan and Victor H. Moll, Involutions and their progenies, arXiv:1406.2356 [math.CO], 2014.
• Carlos M. da Fonseca and Anthony G. Shannon, Telephone numbers extensions, J. Interdisc. Math. (2025) Vol. 28, No. 4, 1573-1580. See p. 1577.

Crossrefs

Partial sums of A000085.

Programs

Magma

I:=[1,2,4]; [n le 3 select I[n] else 2*Self(n-1)-2*Self(n-2)+Self(n-3)+(n-1)*(Self(n-2)-Self(n-3)): n in [1..30]]; // Vincenzo Librandi, Jul 22 2014 // Uses incorrect offset

Maple

a:= proc(n) option remember; 2*a(n-1)+(n-2)*a(n-2)-(n-1)*a(n-3) end:
a(0), a(1), a(2):= 1, 2, 4:
seq(a(n), n=0..30);  # Alois P. Heinz, Oct 19 2014

Mathematica

a[n_] := Sum[StirlingS1[j, k]*2^k*BellB[k, 1/2], {j, 0, n}, {k, 0, j}];
Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Jun 12 2018, after Emanuele Munarini *)

Formula

a(n) = Sum_{k=0..n} A000085(k). - Emanuele Munarini, Aug 31 2017

a(n) ~ exp(sqrt(n) - n/2 - 1/4) * n^(n/2) / sqrt(2). - Vaclav Kotesovec, Jun 12 2018

Extensions

More terms from Vincenzo Librandi, Jul 22 2014