A155857 Row sums of triangle A155856.

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

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*n-k, k)*(n-k)!.

a(n) = Sum_{k=0..n} binomial(n+k, 2*k)*k!. - Paul Barry, May 28 2009

a(n) = (n+1)*a(n-1) -(n-3)*a(n-2) -a(n-3). - R. J. Mathar, Nov 15 2012

a(n) ~ exp(2) * n!. - Vaclav Kotesovec, Feb 08 2014

Mathematica

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

Prog

(Sage) [sum(binomial(2*n-k, k)*factorial(n-k) 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