OFFSET
0,2
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..322
FORMULA
a(n) = n! * [x^n] exp((2*n+1)*x) * (BesselI(0,2*n*x) - BesselI(1,2*n*x)). - Ilya Gutkovskiy, Feb 02 2021
a(n) ~ exp(1/4) * 4^n * n^(n - 3/2) / sqrt(Pi). - Vaclav Kotesovec, Feb 14 2021
MATHEMATICA
A338979[n_] := Sum[n^k*Binomial[n, k]*(2*k)!/(k!*(k + 1)!), {k, 0, n}]; Join[{1}, Table[A338979[n], {n, 1, 14}]] (* Robert P. P. McKone, Jan 31 2021 *)
PROG
(PARI) {a(n) = sum(k=0, n, n^k*binomial(n, k)*(2*k)!/(k!*(k+1)!))}
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jan 31 2021
STATUS
approved