A373651 Expansion of (1 - 2*x + 3*x^2)/(1 - 2*x - 3*x^2)^(5/2).

1, 3, 18, 70, 285, 1071, 3948, 14148, 49815, 172645, 590898, 2000934, 6714799, 22358805, 73947240, 243114552, 795083931, 2588073201, 8389033710, 27089339130, 87174634239, 279653734437, 894553405452, 2853968436900, 9083209323825, 28844069541651, 91405399485078

Offset

0,2

Links

Table of n, a(n) for n=0..26.

Formula

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

a(n) = binomial(n+2,2) * A002426(n).

a(n) = A132885(n+4,2).

a(n) = ((n+2)/n^2) * ((2*n-1)*a(n-1) + 3*(n+1)*a(n-2)).

a(n) ~ 3^(n+1/2) * n^(3/2) / (4 * sqrt(Pi)). - Amiram Eldar, Dec 02 2025

Mathematica

a[n_] := Binomial[n + 2, 2] * GegenbauerC[n, -n, -1/2]; a[0] = 1; Array[a, 30, 0] (* Amiram Eldar, Dec 02 2025*)

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec((1-2*x+3*x^2)/(1-2*x-3*x^2)^(5/2))

Crossrefs

Cf. A002426, A132885, A144087.

Sequence in context: A048899 A337142 A107583 * A157535 A373065 A374487

Adjacent sequences: A373648 A373649 A373650 * A373652 A373653 A373654

Keyword

nonn

Author

Seiichi Manyama, Aug 06 2024

Status

approved