A369599 Expansion of (1/x) * Series_Reversion( x * (1/(1+x)^2 - x^3) ).

1, 2, 5, 15, 54, 223, 993, 4580, 21521, 102563, 495318, 2422302, 11979965, 59824535, 301202673, 1527118720, 7789673832, 39947163395, 205835776301, 1065155017623, 5533253267649, 28844759080896, 150846487065730, 791163319140664, 4160593763997122

Offset: 0

Author

Seiichi Manyama, Jan 27 2024

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A198888, A369600.

Cf. A274378, A274734.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1/(1+x)^2-x^3))/x)

PARI

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

Formula

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