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%I #16 Nov 01 2023 10:00:54
%S 1,1,5,30,210,1595,12791,106574,913562,8004861,71375653,645536234,
%T 5907683486,54605672300,509043322720,4780441915832,45182744331388,
%U 429472919087158,4102806757542542,39370967793387086,379335734835510622,3668220243145708341
%N G.f. satisfies A(x) = 1 + x*A(x)^4*(1 + x).
%H Seiichi Manyama, <a href="/A365178/b365178.txt">Table of n, a(n) for n = 0..988</a>
%F a(n) = Sum_{k=0..n} binomial(4*k+1,k) * binomial(k,n-k)/(4*k+1) = Sum_{k=0..n} binomial(k,n-k) * A002293(k).
%o (PARI) a(n) = sum(k=0, n, binomial(k, n-k)*binomial(4*k, k)/(3*k+1));
%Y Cf. A002294, A365180, A365181, A365182, A365183.
%Y Cf. A364475, A365184.
%Y Cf. A002293, A364987.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Aug 25 2023
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