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A371496 G.f. A(x) satisfies A(x) = 1 / (1 - x*A(x) / (1+x))^4. 5

%I #12 Mar 25 2024 12:06:24

%S 1,4,22,156,1233,10420,92120,841376,7876616,75177492,728784802,

%T 7156081536,71024862452,711383912672,7181295333306,72989746391780,

%U 746308443708928,7671359593228624,79226966456758424,821691132077059740,8554576791134761387

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

%F a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n-1,n-k) * binomial(5*k+3,k)/(k+1).

%F G.f.: A(x) = B(x)^4 where B(x) is the g.f. of A349361.

%o (PARI) a(n) = sum(k=0, n, (-1)^(n-k)*binomial(n-1, n-k)*binomial(5*k+3, k)/(k+1));

%Y Cf. A001006, A371494, A371495.

%Y Cf. A118971, A349361.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Mar 25 2024

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Last modified June 20 23:53 EDT 2024. Contains 373535 sequences. (Running on oeis4.)