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A158442 Triangle T(n,k) = [x^k] n!*(n+1+x^n)*sum_{i=0..n-1} x^i/(i+1) . 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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 22 00:25 EDT 2017. Contains 292326 sequences.