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A245176 a(n) = 2*a(n-1)+(n-2)*a(n-2)-(n-1)*a(n-3) with initial terms (1,2,4). 2
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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 A308030 A252653

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

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Last modified April 8 02:27 EDT 2020. Contains 333312 sequences. (Running on oeis4.)