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

Author

Roger L. Bagula, Dec 28 2008

Keywords

• nonn
• tabl

Comments

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

Examples

			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;
		

Links

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

Programs

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[%]

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) ).

Extensions

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