A366082 -id:A366082 - 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).

A366083 Expansion of (1/x) * Series_Reversion( x*(1-x)^4/(1-x-x^2) ).

Original entry on oeis.org

1, 3, 14, 78, 478, 3109, 21063, 146997, 1049302, 7624330, 56198481, 419155136, 3157356819, 23984387314, 183519131353, 1413099475142, 10941294442694, 85132006090350, 665294548097852, 5219591907202092, 41095469624286421, 324595783790966343

Offset: 0

Seiichi Manyama, Sep 28 2023

nonn

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

Cf. A007440, A108623, A366081, A366082.

Cf. A366050.

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

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