A377240 -id:A377240 - cp's OEIS frontend

A377238 Expansion of 1/(1 - 9x/(1 - 9x)^(1/3))^(1/3).

1, 3, 27, 288, 3267, 38232, 456030, 5511726, 67275765, 827544276, 10243778238, 127471232682, 1593323199828, 19992464465031, 251700257824749, 3178185350410386, 40235213754593325, 510553935341621550, 6492029680359751572, 82705296277037467728, 1055413999621027732986

Offset: 0

Seiichi Manyama, Oct 21 2024

nonn

Cf. A011782, A377237.

Cf. A377240.

a(n) = 9^n*sum(k=0, n, (-1)^k*binomial(-1/3, k)*binomial(n-2*k/3-1, n-k));

a(n) = 9^n * Sum_{k=0..n} (-1)^k * binomial(-1/3,k) * binomial(n-2*k/3-1,n-k).

A377239 Expansion of sqrt(1 + 4x/sqrt(1 - 4x)).

Original entry on oeis.org

1, 2, 2, 8, 22, 80, 268, 976, 3494, 12896, 47556, 177744, 666236, 2515104, 9525976, 36240032, 138269958, 529193152, 2030242708, 7807266512, 30082317460, 116126074400, 449014896040, 1738805527520, 6742758295900, 26180338089280, 101769629532968, 396031222808096, 1542673037902904

Offset: 0

Seiichi Manyama, Oct 21 2024

nonn

Cf. A377240.

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

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

a(n) ~ 2^(2*n) / (Gamma(1/4) * n^(3/4)) * (1 - Gamma(1/4)^2 / (Pi*2^(7/2)*sqrt(n))). - Vaclav Kotesovec, May 03 2025

cp's OEIS Frontend

A377238 Expansion of 1/(1 - 9x/(1 - 9x)^(1/3))^(1/3).

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A377239 Expansion of sqrt(1 + 4x/sqrt(1 - 4x)).

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cp's OEIS Frontend

A377238 Expansion of 1/(1 - 9*x/(1 - 9*x)^(1/3))^(1/3).

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A377239 Expansion of sqrt(1 + 4*x/sqrt(1 - 4*x)).

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Formula

A377238 Expansion of 1/(1 - 9x/(1 - 9x)^(1/3))^(1/3).

A377239 Expansion of sqrt(1 + 4x/sqrt(1 - 4x)).