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A139769
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A triangle of coefficients of the term-like derivatives of A008302 ( Mahonian numbers): p(x,n)=product( sum(d/dx*(x^i),(i,0,m+1)),(m,0,n)).
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0
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1, 1, 2, 1, 4, 7, 6, 1, 6, 18, 36, 49, 46, 24, 1, 8, 33, 94, 204, 354, 497, 562, 501, 326, 120, 1, 10, 52, 188, 528, 1222, 2406, 4102, 6116, 7996, 9132, 9014, 7541, 5116, 2556, 720, 1, 12, 75, 326, 1105, 3106, 7513, 16014, 30558, 52752, 82938, 119230, 156983
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| Row sums are:
{1, 3, 18, 180, 2700, 56700, 1587600, 57153600, 2571912000, 141455160000, 9336040560000}
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FORMULA
| p(x,n)=product( sum(d/dx*(x^i),(i,0,m+1)),(m,0,n)); Out_n,m=Coefficient(p(x,n)).
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EXAMPLE
| {1},
{1, 2},
{1, 4, 7, 6},
{1, 6, 18, 36, 49, 46, 24},
{1, 8, 33, 94, 204, 354, 497, 562, 501, 326, 120},
{1, 10, 52, 188, 528, 1222, 2406, 4102, 6116, 7996, 9132, 9014, 7541, 5116, 2556, 720},
{1, 12, 75, 326, 1105, 3106, 7513, 16014, 30558, 52752, 82938, 119230, 156983,189158, 207915, 207178, 185285, 146308, 99143, 54748, 22212, 5040},
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MATHEMATICA
| a = Table[CoefficientList[Product[Sum[D[x^i, x], {i, 0, m + 1}], {m, 0, n}], x], {n, 0, 10}] Flatten[a]
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CROSSREFS
| Cf. A008302 ( Mahonian numbers).
Sequence in context: A123360 A072015 A123242 * A007839 A184345 A045625
Adjacent sequences: A139766 A139767 A139768 * A139770 A139771 A139772
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KEYWORD
| nonn,uned,tabf
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jun 13 2008
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