A293491 a(n) = n! * [x^n] exp((n+2)*x)*BesselI(0,2*x).

1, 3, 18, 155, 1734, 23877, 390804, 7417377, 160256070, 3885021569, 104465601756, 3086353547433, 99399100528924, 3466411543407555, 130151205663179112, 5235127829223881895, 224609180728848273990, 10239557195235638377449, 494317596005491398892620, 25192788307121307053168673

Offset

0,2

Comments

The n-th term of the n-th binomial transform of A000984.

Links

Table of n, a(n) for n=0..19.

N. J. A. Sloane, Transforms

Formula

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

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

a(n) ~ exp(2) * BesselI(0,2) * n^n. - Vaclav Kotesovec, Oct 16 2017

Mathematica

Table[n! SeriesCoefficient[Exp[(n + 2) x] BesselI[0, 2 x], {x, 0, n}], {n, 0, 19}]
Table[SeriesCoefficient[1/Sqrt[(1 - n x) (1 - (n + 4) x)], {x, 0, n}], {n, 0, 19}]
Join[{1}, Table[Sum[Binomial[n, k] Binomial[2 k, k] n^(n - k), {k, 0, n}], {n, 1, 19}]]
Table[(n + 2)^n HypergeometricPFQ[{1/2 - n/2, -n/2}, {1}, 4/(2 + n)^2], {n, 0, 19}]

Crossrefs

Cf. A000984, A026375, A081671, A098409, A098410, A104454, A186925, A292627, A292632.

Sequence in context: A352647 A145350 A107888 * A370059 A138274 A375945

Adjacent sequences: A293488 A293489 A293490 * A293492 A293493 A293494

Keyword

nonn

Author

Ilya Gutkovskiy, Oct 10 2017

Status

approved