A365839 -id:A365839 - cp's OEIS frontend

A365840 Expansion of (1/x) * Series_Reversion( x*(1-x)^4/(1+x)^2 ).

1, 6, 55, 602, 7263, 93192, 1247636, 17230290, 243669007, 3511010950, 51361157967, 760784343128, 11387857096900, 171988619895216, 2617571721008520, 40105744064042626, 618116513218831407, 9576289414539654450, 149053521972041737413

Offset: 0

Seiichi Manyama, Sep 20 2023

nonn

Cf. A032349, A365839, A365841.

Cf. A278745.

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

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

A365841 Expansion of (1/x) * Series_Reversion( x*(1-x)^5/(1+x)^2 ).

Original entry on oeis.org

1, 7, 75, 959, 13512, 202433, 3164018, 51010415, 842090988, 14163385916, 241843189651, 4181341506009, 73054000725300, 1287786922627590, 22876030462690500, 409093644922627407, 7358978253387945404, 133067774551068558740, 2417375777620571832476

Offset: 0

Seiichi Manyama, Sep 20 2023

nonn

Cf. A032349, A365839, A365840.

Cf. A365766.

a(n) = sum(k=0, n, binomial(5*n+k+4, k)*binomial(2*(n+1), n-k))/(n+1);

a(n) = (1/(n+1)) * Sum_{k=0..n} binomial(5*n+k+4,k) * binomial(2*(n+1),n-k).

cp's OEIS Frontend

A365840 Expansion of (1/x) * Series_Reversion( x*(1-x)^4/(1+x)^2 ).

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