

A155857


Row sums of triangle A155856.


4



1, 2, 6, 23, 107, 590, 3786, 27821, 230869, 2137978, 21873854, 245151555, 2987967551, 39358156310, 557259550034, 8440866957273, 136211005966889, 2333068710452146, 42276699542130166, 808068680469402095
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OFFSET

0,2


COMMENTS

For positive n, a(n) equals the permanent of the n X n matrix with 2's along the main diagonal and the upper diagonal, and 1's everywhere else.  John M. Campbell, Jul 09 2011


LINKS

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


FORMULA

G.f.: 1/(1 x x/(1 x x/(1 x 2*x/(1 x 2*x/(1 x 3*x/(1 x 3*x/(1  ... (continued fraction);
a(n) = Sum_{k=0..n} binomial(2*nk, k)*(nk)!.
a(n) = Sum_{k=0..n} binomial(n+k, 2*k)*k!.  Paul Barry, May 28 2009
a(n) = (n+1)*a(n1) (n3)*a(n2) a(n3).  R. J. Mathar, Nov 15 2012
a(n) ~ exp(2) * n!.  Vaclav Kotesovec, Feb 08 2014


MATHEMATICA

Table[Sum[Binomial[2*nk, k]*(nk)!, {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Feb 08 2014 *)


PROG

(Sage) [sum(binomial(2*nk, k)*factorial(nk) for k in (0..n)) for n in (0..30)] # G. C. Greubel, Jun 05 2021


CROSSREFS

Cf. A155856.
Sequence in context: A071075 A007555 A101053 * A071076 A297196 A112501
Adjacent sequences: A155854 A155855 A155856 * A155858 A155859 A155860


KEYWORD

nonn,easy


AUTHOR

Paul Barry, Jan 29 2009


STATUS

approved



