OFFSET
0,4
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..1665
FORMULA
a(n) = (A120305(n) - (-1)^n)/2. - Vaclav Kotesovec, Apr 03 2019
a(n) ~ 2^(2*n+1) / (9*sqrt(Pi*n)). - Vaclav Kotesovec, Apr 03 2019
G.f.: (1/sqrt(1-4*z)-1+2*z/(1-z^2))/(2*(2+z)). - Sergey Perepechko, Jul 11 2019
MATHEMATICA
Table[Sum[Sum[(-1)^(i + j)*(i + j)!/(2*i!*j!), {i, 1, n}], {j, 1, n}], {n, 0, 30}] (* Vaclav Kotesovec, Apr 03 2019 *)
PROG
(PARI) {a(n) = sum(i=1, n, sum(j=1, n, (-1)^(i+j)*(i+j)!/(2*i!*j!)))}
(PARI) {a(n) = sum(i=2, 2*n, (-1)^i*i!*polcoef(sum(j=1, n, x^j/j!)^2, i))/2} \\ Seiichi Manyama, May 20 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Apr 03 2019
STATUS
approved