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

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..800

T. Amdeberhan, V. H. Moll, Involutions and their progenies, 2014

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

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 *)

Prog

(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

Crossrefs

Sequence in context: A088457 A006786 A125809 * A000117 A338729 A308030

Adjacent sequences: A245173 A245174 A245175 * A245177 A245178 A245179

Keyword

nonn

Author

N. J. A. Sloane, Jul 19 2014

Extensions

More terms from Vincenzo Librandi, Jul 22 2014

Status

approved