OFFSET
0,3
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..317
FORMULA
a(n) = A039755(2*n-1,n-1) for n > 0.
a(n) = (1/((-2)^(n-1) * (n-1)!)) * Sum_{k=0..n-1} (-1)^k * (2*k+1)^(2*n-1) * binomial(n-1,k) for n > 0.
a(n) ~ 2^(3*n - 1) * n^(n - 1/2) / (sqrt(Pi*(1-c)) * (2-c)^n * c^(n - 1/2) * exp(n)), where c = -LambertW(-2*exp(-2)) = -A226775 = 0.4063757399599599... - Vaclav Kotesovec, Oct 02 2021
PROG
(PARI) a(n) = polcoef(1/prod(k=1, n, 1-(2*k-1)*x+x*O(x^n)), n);
(PARI) a(n) = if(n==0, 1, sum(k=0, n-1, (-1)^k*(2*k+1)^(2*n-1)*binomial(n-1, k))/((-2)^(n-1)*(n-1)!));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Sep 28 2021
STATUS
approved