A366090 -id:A366090 - cp's OEIS frontend

A366089 Expansion of (1/x) * Series_Reversion( x*(1-x)^3/(1-x-x^4) ).

1, 2, 7, 30, 142, 715, 3756, 20349, 112864, 637659, 3656775, 21229923, 124531256, 736920158, 4393859967, 26371222935, 159193382812, 965923527255, 5887659026592, 36034716884127, 221362690616841, 1364404640452602, 8435444693847402

Offset: 0

Seiichi Manyama, Sep 28 2023

nonn

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Cf. A366086, A366087, A366088, A366090.

Cf. A366055.

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

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

A366086 Expansion of (1/x) * Series_Reversion( x/(1-x-x^4) ).

Original entry on oeis.org

1, -1, 1, -1, 0, 4, -14, 34, -65, 89, -29, -331, 1464, -4148, 9010, -14366, 9761, 38895, -215015, 674423, -1594973, 2829973, -2732465, -4812567, 36116257, -124617681, 316617081, -611942761, 735416371, 488457845, -6451021289, 24658985649, -66990721867, 139346533259

Offset: 0

Seiichi Manyama, Sep 28 2023

sign

Cf. A366087, A366088, A366089, A366090.

Cf. A366051, A366057.

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

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

A366087 Expansion of (1/x) * Series_Reversion( x*(1-x)/(1-x-x^4) ).

Original entry on oeis.org

1, 0, 0, 0, -1, -1, -1, -1, 3, 8, 14, 21, 7, -40, -134, -291, -389, -188, 710, 2906, 6285, 8931, 5477, -15250, -66359, -149426, -224524, -154288, 336695, 1605033, 3774375, 5887736, 4504451, -7603388, -40495514, -98834842, -159804251, -134317549, 173843349, 1050099387

Offset: 0

Seiichi Manyama, Sep 28 2023

sign

Cf. A366086, A366088, A366089, A366090.

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

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

A366088 Expansion of (1/x) * Series_Reversion( x*(1-x)^2/(1-x-x^4) ).

Original entry on oeis.org

1, 1, 2, 5, 13, 35, 96, 264, 719, 1913, 4875, 11478, 22860, 26044, -77216, -793820, -4394125, -20304455, -85805571, -343282020, -1321898694, -4943906064, -18052305410, -64551823869, -226418611750, -779487689870, -2633172840764, -8717790419014

Offset: 0

Seiichi Manyama, Sep 28 2023

sign

Cf. A366086, A366087, A366089, A366090.

Cf. A366054.

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

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

cp's OEIS Frontend

A366089 Expansion of (1/x) * Series_Reversion( x*(1-x)^3/(1-x-x^4) ).

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A366086 Expansion of (1/x) * Series_Reversion( x/(1-x-x^4) ).

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A366087 Expansion of (1/x) * Series_Reversion( x*(1-x)/(1-x-x^4) ).

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A366088 Expansion of (1/x) * Series_Reversion( x*(1-x)^2/(1-x-x^4) ).

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