A167571 The row sums of triangle A167569.

1, 6, 54, 680, 11160, 226800, 5504688, 155433600, 5006655360, 181193760000, 7279267564800, 321452513141760, 15477343917235200, 806956698772224000, 45293698702796544000, 2723112069367173120000, 174590385277914250444800

Offset: 1

Author

Johannes W. Meijer, Nov 10 2009

Keywords

• easy
• nonn

Comments

A167569 is the lower left triangle of the ED2 array A167560.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..100

Crossrefs

A167560 is the ED2 array.

Equals the row sums of triangle A167569.

Programs

Mathematica

Table[n! (4^n - 1) / (2 n + 1), {n, 1, 20}] (* Vincenzo Librandi, Jun 23 2013 *)

Formula

a(n) = sum(4^(m-1)*(m-1)!*(n+m-1)!/(2*m-1)!, m=1..n).

a(n) = n!*(4^n - 1)/(2*n + 1). - Peter Bala, Jun 21 2013

E.g.f. 1/(4*sqrt(x))*log((1 - 3*x + 2*x^(3/2))/(1 - 3*x - 2*x^(3/2))). - Peter Bala, Jun 21 2013