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A162748 Row sums of factorial-Pascal matrix A162747. 2
1, 2, 5, 14, 42, 132, 430, 1444, 4984, 17648, 64024, 237712, 902416, 3499680, 13853424, 55931168, 230142848, 964460288, 4113656704, 17846729984, 78708574976, 352678567424, 1604739694848, 7411167960576, 34723660917760 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Second binomial transform of aerated factorial numbers. Binomial transform of A084261. Hankel transform is A137704.

LINKS

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

FORMULA

G.f.: 1/(1-2x-x^2/(1-2x-x^2/(1-2x-2x^2/(1-2x-2x^2/(1-2x-3x^2/(1-2x-3x^2/(1-2x-4x^2/(1-2x-... (continued fraction);

a(n)=sum{k=0..floor(n/2), C(n,2k)*2^(n-2k)*F(k+1)}=sum{k=0..n, C(n,k)*2^(n-k)*(k/2)!*(1+(-1)^k)/2}.

a(n)=sum{k=0..n, A161556(n,k)*2^k}. - Paul Barry, Apr 11 2010

E.g.f.: exp(2x)*(1+(sqrt(Pi)/2)*x*exp(x^2/4)*erf(x/2)). - Paul Barry, Sep 17 2010

Apparently -2*a(n) +8*a(n-1) +(n-8)*a(n-2) +2*(2-n)*a(n-3)=0. - R. J. Mathar, Oct 25 2012

a(n) ~ 1/2 * sqrt(Pi*n) * exp(2*sqrt(2*n)-n/2-2) * (n/2)^(n/2) * (1 + 1/(3*sqrt(2*n))). - Vaclav Kotesovec, Aug 15 2013

MATHEMATICA

Table[Sum[Binomial[n, k]*2^(n-k)*(k/2)!*(1+(-1)^k)/2, {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Aug 15 2013 *)

CROSSREFS

Sequence in context: A126567 A125501 A126569 * A061815 A202061 A129086

Adjacent sequences:  A162745 A162746 A162747 * A162749 A162750 A162751

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Jul 12 2009

EXTENSIONS

Minor edits by Vaclav Kotesovec, Jul 22 2015

STATUS

approved

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Last modified February 19 14:52 EST 2018. Contains 299334 sequences. (Running on oeis4.)