login
G.f. satisfies A(x) = ( 1 + x*A(x)^(5/2) / (1 - x)^2 )^2.
3

%I #17 Mar 30 2024 01:40:57

%S 1,2,15,130,1263,13210,145254,1655566,19385489,231803136,2818714210,

%T 34749228048,433317651224,5455934825956,69267925684377,

%U 885756704750960,11397912218979769,147483397060856046,1917785255491649284,25047838828467708506,328444729414573179950

%N G.f. satisfies A(x) = ( 1 + x*A(x)^(5/2) / (1 - x)^2 )^2.

%H Seiichi Manyama, <a href="/A371585/b371585.txt">Table of n, a(n) for n = 0..873</a>

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

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

%Y Cf. A371580, A371583.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Mar 28 2024