OFFSET
0,3
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..1664
FORMULA
a(n) ~ 4^(n+1) / (9*sqrt(Pi*n)). - Vaclav Kotesovec, Apr 05 2019
G.f.: ( 1/(sqrt(1-4*x) * (1-x)) ) * ( x *c(x)/(1 + x *c(x)) ), where c(x) is the g.f. of A000108. - Seiichi Manyama, Jan 30 2023
EXAMPLE
MATHEMATICA
Table[-Sum[Sum[(-1)^(i+j) * (i+j)!/(i!*j!), {i, 0, j-1}], {j, 0, n}], {n, 0, 25}] (* Vaclav Kotesovec, Apr 05 2019 *)
PROG
(PARI) a(n) = -sum(i=0, n, sum(j=i+1, n, (-1)^(i+j)*(i+j)!/(i!*j!)));
(PARI) my(N=30, x='x+O('x^N)); concat(0, Vec((1-sqrt(1-4*x))/(sqrt(1-4*x)*(1-x)*(3-sqrt(1-4*x))))) \\ Seiichi Manyama, Jan 30 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Apr 05 2019
STATUS
approved