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%I #8 Jul 30 2023 09:20:08
%S 1,3,17,153,1621,18732,229103,2915498,38204497,512027945,6985933889,
%T 96705749625,1354868839933,19175008086962,273731258980839,
%U 3936883123412972,56991044183321197,829750943505927435,12142121554514962205,178488780583916045949
%N G.f. satisfies A(x) = (1+x*A(x)^4)/(1-x)^2.
%F a(n) = Sum_{k=0..n} binomial(n+7*k+1,8*k+1) * binomial(4*k,k) / (3*k+1).
%o (PARI) a(n) = sum(k=0, n, binomial(n+7*k+1, 8*k+1)*binomial(4*k, k)/(3*k+1));
%Y Cf. A162477, A364629.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Jul 30 2023