A374675 - OEIS

%I #10 Jul 16 2024 11:34:30

%S 1,2,21,244,3055,40116,544103,7553960,106734195,1528937200,

%T 22143771386,323613807672,4765050473521,70611124679564,

%U 1052084386116915,15750153504353872,236766112174722235,3572264808332407512,54073065371555283968,820886646834780680640

%N a(n) = Sum_{k=0..n} binomial(n+k-1,n) * binomial(n+k,n).

%F a(n) = Sum_{k=0..n} (k/(n+k)) * binomial(n+k,k)^2 for n > 0.

%F a(n) = (n+1) * A259335(n).

%o (PARI) a(n) = sum(k=0, n, binomial(n+k-1, n)*binomial(n+k, n));

%Y Cf. A001791, A374676.

%Y Cf. A112029, A129763, A259335.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Jul 16 2024