%I #15 Jul 27 2023 11:00:01
%S 1,1,2,9,44,226,1241,7093,41666,250260,1529993,9488398,59545909,
%T 377451385,2413157855,15542535697,100753850132,656856027658,
%U 4303970039402,28328599504756,187214549485759,1241775795647609,8263989319451514,55163575187733922
%N G.f. satisfies A(x) = 1 + x*A(x) + x^2*A(x)^7.
%H Seiichi Manyama, <a href="/A364476/b364476.txt">Table of n, a(n) for n = 0..1000</a>
%F a(n) = Sum_{k=0..floor(n/2)} binomial(n+5*k,k) * binomial(n+4*k,n-2*k) / (6*k+1) = Sum_{k=0..floor(n/2)} binomial(n+5*k,7*k) * binomial(7*k,k) / (6*k+1).
%o (PARI) a(n) = sum(k=0, n\2, binomial(n+5*k, k)*binomial(n+4*k, n-2*k)/(6*k+1));
%Y Cf. A000045, A000108, A001006, A182454, A186996, A364472.
%Y Cf. A002296, A364477.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Jul 26 2023