A368936 -id:A368936 - cp's OEIS frontend

A368935 Expansion of (1/x) * Series_Reversion( x * (1-x) * (1-x+x^3) ).

1, 2, 7, 29, 132, 637, 3200, 16554, 87576, 471570, 2575885, 14238003, 79487023, 447540164, 2538352756, 14489355578, 83174465721, 479842193453, 2780625587824, 16178040713569, 94467163314370, 553430174678595, 3251969073086610, 19161172609833540, 113186247571818096

Offset: 0

Seiichi Manyama, Jan 10 2024

nonn

Cf. A129442, A368936, A368937.

Cf. A063033, A368931.

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

my(x='x+O('x^30)); Vec(serreverse(x*(1-x)*(1-x+x^3))/x) \\ Michel Marcus, Jan 10 2024

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

A368937 Expansion of (1/x) * Series_Reversion( x * (1-x) * (1-x+x^5) ).

Original entry on oeis.org

1, 2, 7, 30, 143, 727, 3861, 21165, 118845, 680064, 3951291, 23247874, 138229486, 829292780, 5013767772, 30516496017, 186837457296, 1149894814718, 7110026033305, 44146396259805, 275139524189497, 1720647439298395, 10793938343564655, 67905034046934225

Offset: 0

Seiichi Manyama, Jan 10 2024

nonn

Cf. A129442, A368935, A368936.

Cf. A366046, A368933.

a(n) = sum(k=0, n\5, (-1)^k*binomial(n+k, k)*binomial(3*n-4*k+1, n-5*k))/(n+1);

my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x)*(1-x+x^5))/x)

a(n) = (1/(n+1)) * Sum_{k=0..floor(n/5)} (-1)^k * binomial(n+k,k) * binomial(3*n-4*k+1,n-5*k).

cp's OEIS Frontend

A368935 Expansion of (1/x) * Series_Reversion( x * (1-x) * (1-x+x^3) ).

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A368937 Expansion of (1/x) * Series_Reversion( x * (1-x) * (1-x+x^5) ).

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