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A081126 Binomial transform of n!/floor(n/2)!. 2
1, 2, 5, 16, 53, 206, 817, 3620, 16361, 80218, 401501, 2139512, 11641885, 66599846, 388962953, 2367284236, 14700573137, 94523836850, 619674301621, 4186249123808, 28809504493061, 203556335785342, 1463877667140065 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Row sums of exponential Riordan array [(1+x), x(1+x)]. - Paul Barry, Apr 17 2007

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Guo-Niu Han, Enumeration of Standard Puzzles

Guo-Niu Han, Enumeration of Standard Puzzles [Cached copy]

FORMULA

a(n) = sum(k=0..n, C(n, k)*n!/floor(n/2)!).

a(n) = A018191(n+1).

E.g.f.: (1+x)*exp(x+x^2). - Vladeta Jovovic, Aug 06 2006

a(n) = sum(k=0..n, C(n,k)*k!/floor(k/2)!); a(n) = sum(k=0..n, C(k+1,n-k)*n!/k!). - Paul Barry, Apr 17 2007

Recurrence: (n-2)*a(n) = (n-3)*a(n-1) + 2*(n-1)^2*a(n-2). - Vaclav Kotesovec, Oct 13 2012

a(n) ~ 2^(n/2-1)*exp(sqrt(n/2)-n/2-1/8)*n^(n/2+1/2)*(1+85/96*sqrt(2)/sqrt(n)). - Vaclav Kotesovec, Oct 13 2012

MATHEMATICA

Table[n!*SeriesCoefficient[(1+x)*E^(x+x^2), {x, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Oct 13 2012 *)

CROSSREFS

Cf. A018191, A081125.

Sequence in context: A148397 A148398 A100442 * A018191 A006191 A149959

Adjacent sequences:  A081123 A081124 A081125 * A081127 A081128 A081129

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Mar 07 2003, Apr 17 2007

STATUS

approved

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Last modified November 28 15:19 EST 2014. Contains 250362 sequences.