A379024 Expansion of (1/x) * Series_Reversion( x * ((1 - x - x^2)/(1 + x))^4 ).

1, 8, 100, 1500, 24846, 438064, 8062518, 153117320, 2978260865, 59031215508, 1187987779084, 24210092837648, 498606095949315, 10361291534825800, 216982960825089730, 4574651332139656108, 97018731642209493810, 2068350691029593934000, 44301394943232879298360

Offset

0,2

Links

Table of n, a(n) for n=0..18.

Index entries for reversions of series

Formula

G.f. A(x) satisfies:

(1) A(x) = exp( Sum_{k>=1} A379026(k) * x^k/k ).

(2) A(x) = ( (1 + x*A(x)) * (1 + x*A(x)^(5/4)) )^4.

(3) A(x) = B(x)^4 where B(x) is the g.f. of A239108.

a(n) = (1/(n+1)) * [x^n] ( (1 + x)/(1 - x - x^2) )^(4*(n+1)).

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

Prog

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

Crossrefs

Cf. A007863, A379021, A379023.

Cf. A239108, A379026.

Sequence in context: A208705 A246237 A234513 * A251686 A306032 A274844

Adjacent sequences: A379021 A379022 A379023 * A379025 A379026 A379027

Keyword

nonn

Author

Seiichi Manyama, Dec 14 2024

Status

approved