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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
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.
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
KEYWORD
nonn,easy,tabf
AUTHOR
Paul Curtz, Mar 19 2009
EXTENSIONS
Edited by R. J. Mathar, Apr 09 2009
STATUS
approved