A371914 -id:A371914 - cp's OEIS frontend

A371913 G.f. A(x) satisfies A(x) = 1 - x/A(x)^4 * (1 - A(x) - A(x)^5).

1, 1, 2, 0, -6, 12, 67, -152, -740, 2296, 9017, -35979, -113936, 579516, 1454975, -9493390, -18317155, 157178640, 220172289, -2618995381, -2377680689, 43783556265, 19149194005, -732638868460, 16196837316, 12246524817736, -5891297294673

Offset: 0

Seiichi Manyama, Apr 12 2024

sign

Cf. A349332, A367725, A371914, A371915.

Cf. A371889, A371890.

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

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

A371915 G.f. A(x) satisfies A(x) = 1 - x/A(x)^2 * (1 - A(x) - A(x)^5).

Original entry on oeis.org

1, 1, 4, 17, 80, 414, 2289, 13199, 78306, 474630, 2926744, 18304543, 115837726, 740379722, 4772461321, 30989448116, 202518745795, 1330961476358, 8791022012712, 58325109518331, 388523983047285, 2597516226459845, 17423367396517210, 117223205014488833

Offset: 0

Seiichi Manyama, Apr 12 2024

nonn

Cf. A349332, A367725, A371913, A371914.

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

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

cp's OEIS Frontend

A371913 G.f. A(x) satisfies A(x) = 1 - x/A(x)^4 * (1 - A(x) - A(x)^5).

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