A026935 a(n) = Sum_{k=0..n-2} T(n,k) * T(n,k+2), with T given by A008288.

1, 10, 75, 500, 3149, 19214, 115031, 680424, 3992921, 23305234, 135514019, 785892316, 4549048229, 26295995926, 151857925039, 876366840784, 5055045581745, 29148894792730, 168045778127355, 968679251764676, 5583525654107645, 32183666525389086, 185514611981021959

Offset: 2

Author

Clark Kimberling

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 2..500

Crossrefs

Cf. A008288.

Programs

Mathematica

A008288[n_, k_]:= Binomial[n, k]*Hypergeometric2F1[-k, k-n, -n, -1];
A026935[n_]:= Sum[A008288[n, k]*A008288[n, k+2], {k, 0, n-2}];
Table[A026935[n], {n, 2, 40}] (* G. C. Greubel, May 25 2021 *)

Sage

@CachedFunction
def A008288(n,k): return sum(binomial(n-j, j)*binomial(n-2*j, k-j) for j in (0..k))
def A026935(n): return sum(A008288(n, k)*A008288(n, k+2) for k in (0..n-2))
[A026935(n) for n in (2..40)] # G. C. Greubel, May 25 2021

Extensions

More terms from Sean A. Irvine, Oct 17 2019