A349312 -id:A349312 - cp's OEIS frontend

A366366 G.f. satisfies A(x) = (1 + x/A(x)^4)/(1 - x).

1, 2, -6, 58, -574, 6402, -75878, 939290, -12000318, 157050178, -2094657926, 28368411194, -389079656446, 5393118559938, -75431624084838, 1063251390845338, -15088643098754942, 215396586102923138, -3091050571516120582, 44566089825496186170

Offset: 0

Seiichi Manyama, Oct 08 2023

sign

Cf. A346626, A349310, A349311, A349312, A349313, A349314, A366363, A366364, A366365.

Cf. A366359.

a(n) = (-1)^(n-1)*sum(k=0, n, binomial(5*k-1, k)*binomial(4*k-1, n-k)/(5*k-1));

a(n) = (-1)^(n-1) * Sum_{k=0..n} binomial(5*k-1,k) * binomial(4*k-1,n-k)/(5*k-1).

A371932 G.f. A(x) satisfies A(x) = 1 + x/A(x)^2 * (1 + A(x)^5).

Original entry on oeis.org

1, 2, 2, 26, 50, 706, 1650, 24282, 62370, 940610, 2554530, 39150810, 110311762, 1709993346, 4945525650, 77314273562, 228002115650, 3587763069826, 10741365151810, 169903043416730, 514833595840370, 8177978884039490, 25025386537586610

Offset: 0

Seiichi Manyama, Apr 13 2024

nonn

Cf. A364393, A364394, A364396, A364397, A366364, A371893.

Cf. A349312, A366268, A371562, A371341.

a(n) = if(n==0, 1, (-1)^(n-1)*sum(k=0, n, binomial(n, k)*binomial(3*n-5*k-2, n-1))/n);

a(n) = (-1)^(n-1) * (1/n) * Sum_{k=0..n} binomial(n,k) * binomial(3*n-5*k-2,n-1) for n > 0.

a(n) == 2 (mod 8) for n > 0. - Hugo Pfoertner, Apr 13 2024

cp's OEIS Frontend

A366366 G.f. satisfies A(x) = (1 + x/A(x)^4)/(1 - x).

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