OFFSET
0,2
COMMENTS
The n-th term of the n-th binomial transform of A000984.
LINKS
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
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Oct 10 2017
STATUS
approved