A366432 - OEIS

%I #11 Oct 10 2023 05:11:21

%S 1,1,7,49,378,3136,27363,247597,2302511,21872361,211336755,2070577285,

%T 20522662832,205411356794,2073258075175,21078157565623,

%U 215658366319375,2218853063356937,22942886758494094,238284942878492146,2484736162773443446

%N G.f. A(x) satisfies A(x) = 1 + x * (A(x) / (1 - x))^(7/2).

%F a(n) = Sum_{k=0..n} binomial(n+5*k/2-1,n-k) * binomial(7*k/2,k) / (5*k/2+1).

%o (PARI) a(n) = sum(k=0, n, binomial(n+5*k/2-1, n-k)*binomial(7*k/2, k)/(5*k/2+1));

%Y Partial sums give A366401.

%Y Cf. A366431, A366433, A366434, A366435, A366436, A366437.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Oct 09 2023