OFFSET
0,2
COMMENTS
The n-th term of the n-th binomial transform of A001006.
LINKS
Robert Israel, Table of n, a(n) for n = 0..300
N. J. A. Sloane, Transforms
FORMULA
a(n) = [x^n] (1 - (n + 1)*x - sqrt((1 - (n - 1)*x)*(1 - (n + 3)*x)))/(2*x^2).
a(n) ~ exp(1) * BesselI(1,2) * n^n. - Vaclav Kotesovec, Nov 13 2017
MAPLE
S:= series(exp((n+1)*x)*BesselI(1, 2*x)/x, x, 102):
seq(simplify(n!*coeff(S, x, n)), n=0..100); # Robert Israel, Nov 03 2017
MATHEMATICA
Table[n! SeriesCoefficient[Exp[(n + 1) x] BesselI[1, 2 x]/x, {x, 0, n}], {n, 0, 19}]
Table[SeriesCoefficient[(1 - (n + 1) x - Sqrt[(1 - (n - 1) x) (1 - (n + 3) x)])/(2 x^2), {x, 0, n}], {n, 0, 19}]
Table[(n + 1)^n HypergeometricPFQ[{1/2 - n/2, -n/2}, {2}, 4/(n + 1)^2], {n, 0, 19}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Nov 02 2017
STATUS
approved