A366083 -id:A366083 - cp's OEIS frontend

A366081 Expansion of (1/x) * Series_Reversion( x*(1-x)^2/(1-x-x^2) ).

1, 1, 1, 0, -5, -22, -68, -165, -285, -96, 1892, 10574, 38436, 107175, 217063, 165232, -1150565, -7780744, -31173680, -94537100, -212903852, -239418048, 788015576, 6734057510, 29396759220, 95418332383, 233697161887, 334222633632, -514863450175, -6299672869750

Offset: 0

Seiichi Manyama, Sep 28 2023

sign

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

Cf. A007440, A108623, A366082, A366083.

Cf. A109081.

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

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

A366082 Expansion of (1/x) * Series_Reversion( x*(1-x)^3/(1-x-x^2) ).

Original entry on oeis.org

1, 2, 6, 21, 79, 308, 1219, 4826, 18857, 71574, 257553, 837114, 2140496, 1379550, -35589730, -370646635, -2719034151, -17429175486, -103771133876, -588804389677, -3225403649859, -17180039158530, -89342552789741, -454604059204324, -2265246385921936

Offset: 0

Seiichi Manyama, Sep 28 2023

sign

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

Cf. A007440, A108623, A366081, A366083.

Cf. A366049.

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

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

cp's OEIS Frontend

A366081 Expansion of (1/x) * Series_Reversion( x*(1-x)^2/(1-x-x^2) ).

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