A369616 Expansion of (1/x) * Series_Reversion( x / (1/(1-x)^2 + x) ).

1, 3, 12, 58, 314, 1824, 11107, 69955, 451918, 2977834, 19936332, 135225006, 927267595, 6417580459, 44770275705, 314489676679, 2222549047262, 15791353483602, 112734135824404, 808247711066688, 5817056710700424, 42012120642574732, 304384379305912686

Offset

0,2

Links

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

Index entries for reversions of series

Formula

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

D-finite with recurrence 2*(n+1)*(2*n+1)*a(n) +3*(-13*n^2+1)*a(n-1) +33*(2*n-1)*(n-1)*a(n-2) -31*(n-1)*(n-2)*a(n-3)=0. - R. J. Mathar, Jan 28 2024

Maple

A369616 := proc(n)
    add(binomial(n+1, k) * binomial(3*n-3*k+1, n-k), k=0..n) ;
    %/(n+1) ;
end proc;
seq(A369616(n), n=0..70) ; # R. J. Mathar, Jan 28 2024

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x/(1/(1-x)^2+x))/x)
(PARI) a(n) = sum(k=0, n, binomial(n+1, k)*binomial(3*n-3*k+1, n-k))/(n+1);

Crossrefs

Cf. A007317, A369617, A370844.

Cf. A006013, A274734.

Sequence in context: A122677 A038177 A163047 * A372378 A369594 A369403

Adjacent sequences: A369613 A369614 A369615 * A369617 A369618 A369619

Keyword

nonn

Author

Seiichi Manyama, Jan 27 2024

Status

approved