A376546 - OEIS

%I #7 Sep 27 2024 16:33:48

%S 1,0,0,0,1,1,0,0,4,8,4,0,22,66,66,22,140,560,840,560,1109,4845,9690,

%T 9690,11929,43473,106260,141680,160080,419244,1137304,1883700,2304432,

%U 4496076,12157236,23614812,32813500,53821332,132821856,285795696,451409380

%N G.f. A(x) satisfies A(x) = 1 + x^4*(1+x)*A(x)^4.

%F a(n) = Sum_{k=0..floor(n/4)} binomial(k,n-4*k) * binomial(4*k,k)/(3*k+1).

%o (PARI) a(n) = sum(k=0, n\4, binomial(k, n-4*k)*binomial(4*k, k)/(3*k+1));

%Y Cf. A017827, A366589, A375691, A376487.

%K nonn

%O 0,9

%A _Seiichi Manyama_, Sep 27 2024