OFFSET
0,3
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 01 2021
a(n) ~ exp(-1/4) * 4^n * n^(n - 3/2) / sqrt(Pi). - Vaclav Kotesovec, Feb 14 2021
MATHEMATICA
a[0] = 1; a[n_] := (-1)^n * Sum[(-n)^k * Binomial[n, k] * CatalanNumber[k], {k, 0, n}]; Array[a, 15, 0] (* Amiram Eldar, Feb 01 2021 *)
PROG
(PARI) {a(n) = (-1)^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