A171534 Triangle read by rows: T(n,k)=binomial(2*n*k+k,2)/(2*n+1).

1, 2, 9, 3, 13, 30, 4, 17, 39, 70, 5, 21, 48, 86, 135, 6, 25, 57, 102, 160, 231, 7, 29, 66, 118, 185, 267, 364, 8, 33, 75, 134, 210, 303, 413, 540, 9, 37, 84, 150, 235, 339, 462, 604, 765, 10, 41, 93, 166, 260, 375, 511, 668, 846, 104

Offset: 1

Author

Roger L. Bagula, Dec 11 2009

Keywords

• nonn
• tabl

Comments

Row sums are: 1, 11, 46, 130, 295, 581, 1036, 1716, 2685, 4015,... see A006324

Examples

			1;
2, 9;
3, 13, 30;
4, 17, 39, 70;
5, 21, 48, 86, 135;
6, 25, 57, 102, 160, 231;
7, 29, 66, 118, 185, 267, 364;
8, 33, 75, 134, 210, 303, 413, 540;
9, 37, 84, 150, 235, 339, 462, 604, 765;
10, 41, 93, 166, 260, 375, 511, 668, 846, 1045;
		

References

• J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 145.

Crossrefs

Cf. A008406

Programs

Mathematica

Table[Table[Binomial[2*n*k + k, 2]/(2*n + 1), {k, 1, n}], {n, 1, 10}]
Flatten[%]

Formula

T(n,k)=binomial(2*n*k + k, 2)/(2*n + 1).

Extensions

Introduced OEIS notational standards and keyword:tabl - The Assoc. Editors of the OEIS, Dec 15 2009