A151709 Row sums of A156741.

1, 2, 192, 14632, 5451140, 2216555772, 2201283594512, 2563699840815752, 5239330894956743702, 12738172416005805235262, 45354957806572334315266802, 190794310975336315988205573422, 1056059186013450690759502943569093, 6805676661977149073551721890947184830

Offset: 0

Author

N. J. A. Sloane, Jun 06 2009

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..200

Crossrefs

Cf. A156741.

Programs

Mathematica

A156741[n_, k_]:= Round[Product[Binomial[2*(n+j), 2*(k+j)]/Binomial[2*(n-k+j), 2*j], {j, 0, 8}]];
A151709[n_]:= A151709[n]= Sum[A156741[n, k], {k,0,n}];
Table[A151709[n], {n, 0, 30}] (* G. C. Greubel, Jun 19 2021 *)

Sage

def A156741(n, k): return round( product( binomial(2*(n+j), 2*(k+j))/binomial(2*(n-k+j), 2*j) for j in (0..8)) )
def A151709(n): return sum( A156741(n, k) for k in (0..n) )
[A151709(n) for n in (0..30)] # G. C. Greubel, Jun 19 2021

Formula

a(n) = Sum_{k=0..n} A156741(n, k).

Extensions

Terms a(11) onward added by G. C. Greubel, Jun 19 2021