A361932 -id:A361932 - cp's OEIS frontend

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

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).

A364403 G.f. A(x) satisfies A(x) = 1 + x^4 * (A(x) / (1 - x))^3.

Original entry on oeis.org

1, 0, 0, 0, 1, 3, 6, 10, 18, 39, 91, 204, 435, 919, 1992, 4434, 9947, 22215, 49455, 110480, 248505, 561930, 1273610, 2889666, 6566736, 14959083, 34163511, 78182700, 179201199, 411325125, 945512784, 2176710450, 5018195400, 11583688995, 26770164919

Offset: 0

Seiichi Manyama, Oct 15 2023

nonn

Partial sums give A364552.

Cf. A000245, A213282, A361932.

a(n) = sum(k=0, n\4, binomial(n-k-1, n-4*k)*binomial(3*k, k)/(2*k+1));

a(n) = Sum_{k=0..floor(n/4)} binomial(n-k-1,n-4*k) * binomial(3*k,k) / (2*k+1).

cp's OEIS Frontend

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

Views

Author

Keywords

Crossrefs

Programs

PARI

Formula