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Search: id:A153512
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| A153512 |
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A triangular Gamma-Binomial sequence: t(n,m)=(2*n + 1)!!*Pi*Gamma[2*n + 2]/(n!*4^(n + 1)*Gamma[m + 3/2]*Gamma[n + 3/2 - m]). |
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+0
1
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| 1, 3, 3, 15, 25, 15, 105, 245, 245, 105, 945, 2835, 3969, 2835, 945, 10395, 38115, 68607, 68607, 38115, 10395, 135135, 585585, 1288287, 1656369, 1288287, 585585, 135135, 2027025, 10135125, 26351325, 41409225, 41409225, 26351325, 10135125
(list; table; graph; listen)
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OFFSET
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0,2
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COMMENT
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Row sums are:
{1, 6, 55, 700, 11529, 234234, 5674383, 159845400, 5136642225, 185498257230,
7438043704455}.
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FORMULA
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t(n,m)=(2*n + 1)!!*Pi*Gamma[2*n + 2]/(n!*4^(n + 1)*Gamma[m + 3/2]*Gamma[n + 3/2 - m]).
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EXAMPLE
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{1},
{3, 3},
{15, 25, 15},
{105, 245, 245, 105},
{945, 2835, 3969, 2835, 945},
{10395, 38115, 68607, 68607, 38115, 10395},
{135135, 585585, 1288287, 1656369, 1288287, 585585, 135135},
{2027025, 10135125, 26351325, 41409225, 41409225, 26351325, 10135125, 2027025},
{34459425, 195270075, 585810225, 1087933275, 1329696225, 1087933275, 585810225, 195270075, 34459425},
{654729075, 4146617475, 14098499415, 30211070175, 43638212475, 43638212475, 30211070175, 14098499415, 4146617475, 654729075}, {13749310575, 96245174025, 365731661295, 888205463145, 1480342438575, 1749495609225, 1480342438575, 888205463145, 365731661295, 96245174025, 13749310575}
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MATHEMATICA
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T[n_, m_] = (2*n + 1)!!* Pi*Gamma[2*n + 2]/(n!*4^(n + 1)*Gamma[m + 3/2]*Gamma[n + 3/2 - m]);
Table[Table[T[n, m], {m, 0, n}], {n, 0, 10}];
Flatten[%]
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CROSSREFS
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Sequence in context: A133221 A110096 A157526 this_sequence A127328 A002891 A089875
Adjacent sequences: A153509 A153510 A153511 this_sequence A153513 A153514 A153515
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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 28 2008
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