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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) * k! / floor(k/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 May 26 13:05 EDT 2019. Contains 323586 sequences. (Running on oeis4.)