A158442 Triangle T(n,k) = [x^k] n!*(n+1+x^n)*Sum_{i=0..n-1} x^i/(i+1).

2, 1, 6, 3, 2, 1, 24, 12, 8, 6, 3, 2, 120, 60, 40, 30, 24, 12, 8, 6, 720, 360, 240, 180, 144, 120, 60, 40, 30, 24, 5040, 2520, 1680, 1260, 1008, 840, 720, 360, 240, 180, 144, 120, 40320, 20160, 13440, 10080, 8064, 6720, 5760, 5040, 2520, 1680, 1260, 1008, 840, 720, 362880

Offset: 1

Author

Paul Curtz, Mar 19 2009

Keywords

• nonn
• easy
• tabf

Comments

The coefficient in front of x^k of the polynomial n!*(n+1+x^n)*Sum_{i=0..n-1} x^i/(i+1), columns k=0..2n-1.

Examples

			The triangle starts
    2,  1;
    6,  3,  2,  1;
   24, 12,  8,  6,  3,  2;
  120, 60, 40, 30, 24, 12,  8,  6;
		

Crossrefs

Cf. A130679 (table Q), A158442.

Programs

Maple

P := proc(n,k) (n+1+x^n)*add( x^i/(i+1),i=0..n-1) ; coeftayl(expand(%),x=0,k) ; end:
T := proc(n,k) n!*P(n,k) ; end:
for n from 1 to 10 do for k from 0 to 2*n-1 do printf("%d,",T(n,k)) ; od: od: # R. J. Mathar, Apr 09 2009

Formula

Row sums: (n+2)*A000254(n).

Extensions

Edited by R. J. Mathar, Apr 09 2009