A307349 a(n) = Sum_{i=1..n} Sum_{j=1..n} (-1)^(i+j) * (i+j)!/(2!*i!*j!).

0, 1, 1, 5, 15, 56, 203, 757, 2839, 10736, 40821, 155948, 598065, 2301118, 8878591, 34340085, 133100055, 516851528, 2010358061, 7831136920, 30546063745, 119291436738, 466379022561, 1825168170620, 7149316835465, 28027993191706, 109965636641173

Offset: 0

Author

Seiichi Manyama, Apr 03 2019

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..1665

Crossrefs

Cf. A048775, A120305, A307350, A307351.

Programs

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 *)

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

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