A366645 -id:A366645 - cp's OEIS frontend

A364410 G.f. A(x) satisfies A(x) = 1 + x^2 * (A(x) / (1 - x))^4.

1, 0, 1, 4, 14, 52, 201, 800, 3260, 13536, 57068, 243664, 1051512, 4579088, 20097526, 88810872, 394811696, 1764477304, 7923087616, 35728412152, 161731039076, 734646128920, 3347600839252, 15298276784648, 70097391229500, 321974115549256, 1482242974320685

Offset: 0

Seiichi Manyama, Oct 15 2023

nonn

Partial sums give A186996.

Cf. A213336, A366645, A366646.

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

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

A364410 G.f. A(x) satisfies A(x) = 1 + x^2 * (A(x) / (1 - x))^4.

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