A153512 Triangle T(n,m) = (A006882(2*n + 1))^2 / ( A006882(2*m+1) * A006882(2*n-2*m+1) ).

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

Offset

0,2

Comments

Row sums are 1, 6, 55, 700, 11529, 234234, 5674383, 159845400, 5136642225, 185498257230, 7438043704455...

Links

G. C. Greubel, Table of n, a(n) for n = 0..1034

Formula

T(n,m)= A006882(2*n + 1)*Pi*Gamma(2*n + 2)/(n!*4^(n + 1)*Gamma(m + 3/2)*Gamma(n + 3/2 - m) ).

Example

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;

Mathematica

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[%]

Crossrefs

Sequence in context: A157526 A208229 A269956 * A369358 A127328 A002891

Adjacent sequences: A153509 A153510 A153511 * A153513 A153514 A153515

Keyword

nonn,tabl

Author

Roger L. Bagula, Dec 28 2008

Extensions

Definition replaced by an integer expression by the Assoc. Editors of the OEIS, Feb 24 2010

Status

approved