A364410 -id:A364410 - cp's OEIS frontend

A366645 G.f. A(x) satisfies A(x) = 1 + x^3 * (A(x) / (1 - x))^4.

1, 0, 0, 1, 4, 10, 24, 67, 200, 586, 1704, 5049, 15232, 46284, 141240, 433696, 1340500, 4164830, 12993792, 40697472, 127941300, 403561902, 1276763096, 4050430502, 12882398456, 41068966204, 131211997496, 420056152498, 1347272602056, 4328764460928, 13931034024536

Offset: 0

Seiichi Manyama, Oct 15 2023

nonn

Partial sums give A215340.

Cf. A213336, A364410, A366646.

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

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

A366646 G.f. A(x) satisfies A(x) = 1 + (x * A(x) / (1 - x))^4.

Original entry on oeis.org

1, 0, 0, 0, 1, 4, 10, 20, 39, 88, 228, 600, 1507, 3652, 8866, 22100, 56365, 144656, 369784, 942480, 2408934, 6196280, 16026652, 41571640, 107959654, 280708560, 731349400, 1910098320, 4999759830, 13109582376, 34421585844, 90500370760, 238272324682

Offset: 0

Seiichi Manyama, Oct 15 2023

nonn

Partial sums give A127902.
Cf. A213336, A364410, A366645.
Cf. A002026, A361932.

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

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

cp's OEIS Frontend

A366645 G.f. A(x) satisfies A(x) = 1 + x^3 * (A(x) / (1 - x))^4.

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