A264409 a(n) = Sum_{k=0..n} binomial(n, k) * binomial((n-k)*k, k).

1, 1, 3, 10, 53, 376, 3187, 31312, 348833, 4318804, 58583231, 862021084, 13650998473, 231123405124, 4160680867085, 79272259679386, 1592221255517713, 33599025754872240, 742661269363444447, 17149370461633306924, 412742027009797487561, 10331628852664232678356, 268469799828424474556585, 7229580560131818394109850, 201438863633591604857727001

Offset: 0

Author

Paul D. Hanna, Nov 18 2015

Keywords

• nonn

Examples

			a(0) = 1;
a(1) = 1*C(0,0) + 1*C(0,1) = 1;
a(2) = 1*C(0,0) + 2*C(1,1) + 1*C(0,2) = 1 + 2*1 + 0 = 3;
a(3) = 1*C(0,0) + 3*C(2,1) + 3*C(2,2) + 1*C(0,3) = 1 + 3*2 + 3*1 + 0 = 10;
a(4) = 1*C(0,0) + 4*C(3,1) + 6*C(4,2) + 4*C(3,3) + 1*C(0,4) = 1 + 4*3 + 6*6 + 4 + 0 = 53; ...
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..468

Programs

Mathematica

Table[Sum[Binomial[n, k] * Binomial[(n-k)*k, k], {k,0,n}], {n,0,20}] (* Vaclav Kotesovec, Aug 22 2017 *)

PARI

{a(n) = sum(k=0, n, binomial(n, k)*binomial((n-k)*k, k))}
for(n=0,30,print1(a(n),", "))