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A158442
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Triangle T(n,k) = [x^k] n!*(n+1+x^n)*sum_{i=0..n-1} x^i/(i+1) .
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1
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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; internal format)
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OFFSET
| 1,1
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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.
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FORMULA
| Row sums: (n+2)*A000254(n).
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EXAMPLE
| The triangle starts
2,1;
6,3,2,1;
24,12,8,6,3,2;
120,60,40,30,24,12,8,6;
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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
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CROSSREFS
| Cf. A130679 (table Q), A158442.
Sequence in context: A173333 A096334 A107867 * A120435 A125901 A094307
Adjacent sequences: A158439 A158440 A158441 * A158443 A158444 A158445
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KEYWORD
| nonn,easy,tabf
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AUTHOR
| Paul Curtz (bpcrtz(AT)free.fr), Mar 19 2009
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EXTENSIONS
| Edited by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 09 2009
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