OFFSET
0,2
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..195
FORMULA
a(n) = Stirling2(2*n,n) * n! * binomial(2*n,n).
a(n) ~ n^(2*n - 1/2) * 2^(4*n) / (sqrt(Pi*(1-c)) * c^n * (2-c)^n * exp(2*n)), where c = -LambertW(-2*exp(-2)) = -A226775 = 0.4063757399599599... - Vaclav Kotesovec, Jun 10 2017
EXAMPLE
a(1) = 2: (1,1), (2,2).
MAPLE
b:= proc(n, k) option remember; `if`(k=n, n!,
`if`(k=0, 0, n*(b(n-1, k-1)+b(n-1, k)*k/(n-k))))
end:
a:= n-> b(2*n, n):
seq(a(n), n=0..15);
MATHEMATICA
Table[StirlingS2[2*n, n]*(2*n)!/n!, {n, 0, 20}] (* Vaclav Kotesovec, Jun 10 2017 *)
PROG
(PARI) a(n)=stirling(2*n, n, 2)*n!*binomial(2*n, n); \\ Indranil Ghosh, Jul 04 2017
(Python)
from mpmath import *
mp.dps=100
def a(n): return int(stirling2(2*n, n)*fac(n)*binomial(2*n, n))
print([a(n) for n in range(21)]) # Indranil Ghosh, Jul 04 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jun 07 2017
STATUS
approved