A379546 Expansion of (1/x) * Series_Reversion( x / ( (1+x)^2 * (1+2*x)^3 ) ).

1, 8, 89, 1150, 16190, 240966, 3729185, 59404934, 967608590, 16041857672, 269807678442, 4592326407908, 78954271935856, 1369136489157250, 23918810207745777, 420575805001923782, 7437459126200243030, 132190772588551036800, 2360148586461490077870

Offset

0,2

Links

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

Index entries for reversions of series

Formula

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

a(n) = A371669(n+1)/2 = (1/(n+1)) * Sum_{k=0..floor(n/2)} 2^(n-2*k) * binomial(n+1,k) * binomial(4*(n+1)-k,n-2*k).

a(n) = (1/(n+1)) * [x^n] ( (1+x)^2 * (1+2*x)^3 )^(n+1).

Prog

(PARI) my(N=20, x='x+O('x^N)); Vec(serreverse(x/((1+x)^2*(1+2*x)^3))/x)
(PARI) a(n) = sum(k=0, n\2, 2^(n-2*k)*binomial(n+1, k)*binomial(4*(n+1)-k, n-2*k))/(n+1);

Crossrefs

Cf. A003168, A371406, A379547.

Cf. A371398, A379522.

Cf. A371669.

Sequence in context: A208265 A184756 A295244 * A264072 A303056 A131655

Adjacent sequences: A379543 A379544 A379545 * A379547 A379548 A379549

Keyword

nonn

Author

Seiichi Manyama, Dec 25 2024

Status

approved