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

1,1

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.

Links

Table of n, a(n) for n=1..57.

Formula

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

Example

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

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

Crossrefs

Cf. A130679 (table Q), A158442.

Sequence in context: A221623 A096334 A107867 * A252095 A120435 A125901

Adjacent sequences: A158439 A158440 A158441 * A158443 A158444 A158445

Keyword

nonn,easy,tabf

Author

Paul Curtz, Mar 19 2009

Extensions

Edited by R. J. Mathar, Apr 09 2009

Status

approved