A368972 Expansion of (1/x) * Series_Reversion( x * (1-x+x^3)^3 ).

1, 3, 15, 88, 564, 3819, 26851, 194025, 1431498, 10735548, 81580008, 626697786, 4858272450, 37954323885, 298487957670, 2361025981335, 18770449480056, 149897172319290, 1201831832357041, 9670416882346848, 78062823843714528, 631988009034161246

Offset: 0

Author

Seiichi Manyama, Jan 10 2024

Keywords

• sign

Comments

a(702) is negative.

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..1000
• Index entries for reversions of series

Crossrefs

Cf. A368964.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x+x^3)^3)/x)

PARI

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

Formula

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