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Search: id:A153274
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| A153274 |
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A Pochhammer function-based triangular sequence: w(n,m,j)=m^(n + 1)*Pochhammer[j/m,n+1]; t(n,m)=sum_coefficients(w(n,m,j) in j). |
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+0
1
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| 2, 6, 15, 24, 105, 280, 120, 945, 3640, 9945, 720, 10395, 58240, 208845, 576576, 5040, 135135, 1106560, 5221125, 17873856, 49579075, 40320, 2027025, 24344320, 151412625, 643458816, 2131900225, 5925744000, 362880, 34459425, 608608000
(list; table; graph; listen)
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OFFSET
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0,1
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COMMENT
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Row sums are:
{2, 21, 409, 14650, 854776, 73920791, 8878927331, 1413788600036,
288152651134776, 73152069870215127}.
The first column is the factorials starting at 2.
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FORMULA
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w(n,m,j)=m^(n + 1)*Pochmammer[j/m,n+1]; w(n,m,j)=Product[m*k + j, {k, 0, n}]; t(n,m)=sum_coefficients(w(n,m,j) in j).
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EXAMPLE
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{2},
{6, 15},
{24, 105, 280},
{120, 945, 3640, 9945},
{720, 10395, 58240, 208845, 576576},
{5040, 135135, 1106560, 5221125, 17873856, 49579075},
{40320, 2027025, 24344320, 151412625, 643458816, 2131900225, 5925744000},
{362880, 34459425, 608608000, 4996616625, 26381811456, 104463111025, 337767408000, 939536222625},
{3628800, 654729075, 17041024000, 184874815125, 1213563326976, 5745471106375, 21617114112000, 68586144251625, 190787784140800},
{39916800, 13749310575, 528271744000, 7579867420125, 61891729675776, 350473737488875, 1534815101952000, 5555477684381625, 17361688356812800, 48279601331512551}
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MATHEMATICA
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Clear[t, n, m, j, k];
t[n_, m_] = Product[m*k + j, {k, 0, n}]
Table[Table[Apply[Plus, CoefficientList[t[n, m], j]], {m, 1, n}], {n, 1, 10}];
Flatten[%]
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CROSSREFS
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Sequence in context: A090979 A050508 A033298 this_sequence A091766 A138621 A163061
Adjacent sequences: A153271 A153272 A153273 this_sequence A153275 A153276 A153277
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KEYWORD
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nonn,uned,tabl
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Dec 22 2008
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