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
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
Comments