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A139769 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)). 0

%I #2 Mar 30 2012 17:34:26

%S 1,1,2,1,4,7,6,1,6,18,36,49,46,24,1,8,33,94,204,354,497,562,501,326,

%T 120,1,10,52,188,528,1222,2406,4102,6116,7996,9132,9014,7541,5116,

%U 2556,720,1,12,75,326,1105,3106,7513,16014,30558,52752,82938,119230,156983

%N 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)).

%C Row sums are:

%C {1, 3, 18, 180, 2700, 56700, 1587600, 57153600, 2571912000, 141455160000, 9336040560000}

%F p(x,n)=product( sum(d/dx*(x^i),(i,0,m+1)),(m,0,n)); Out_n,m=Coefficient(p(x,n)).

%e {1},

%e {1, 2},

%e {1, 4, 7, 6},

%e {1, 6, 18, 36, 49, 46, 24},

%e {1, 8, 33, 94, 204, 354, 497, 562, 501, 326, 120},

%e {1, 10, 52, 188, 528, 1222, 2406, 4102, 6116, 7996, 9132, 9014, 7541, 5116, 2556, 720},

%e {1, 12, 75, 326, 1105, 3106, 7513, 16014, 30558, 52752, 82938, 119230, 156983,189158, 207915, 207178, 185285, 146308, 99143, 54748, 22212, 5040},

%t a = Table[CoefficientList[Product[Sum[D[x^i, x], {i,0, m + 1}], {m, 0, n}], x], {n, 0, 10}] Flatten[a]

%Y Cf. A008302 ( Mahonian numbers).

%K nonn,uned,tabf

%O 1,3

%A _Roger L. Bagula_, Jun 13 2008

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