A137941 G.f.: exp(x) = Product_{n>=1} [1 + a(2n-1)*x^(2n-1)/(2n-1)! + a(2n)*x^(2n)/(2n)! ].

1, 1, 1, -3, 6, 10, -195, 945, -3080, 17136, 37170, -796950, 3880800, 122007600, -2380685307, 18531377865, -136619683200, 942469528000, 723819456360, -118481659031736, 1884943573381440, -16067035945724400, -323306803861791750, 15940746503392961250

Offset: 1

Author

Paul D. Hanna, Feb 23 2008

Keywords

• sign

Comments

a(n) appears to be divisible by (n-1)(n-2)/2 for n>2.

Examples

			exp(x) = (1 + 1*x + 1*x^2/2!) * (1 + 1*x^3/3! - 3*x^4/4!) * (1 + 6*x^5/5! + 10*x^6/6!) * (1 - 195*x^7/7! + 945*x^8/8!) *...
		

Crossrefs

Cf. A137852.

Programs

PARI

{a(n)=if(n<1, 0, n!*polcoeff(exp(x +x*O(x^n))/prod(k=1, (n-1)\2, 1+a(2*k-1)*x^(2*k-1)/(2*k-1)!+a(2*k)*x^(2*k)/(2*k)! +x*O(x^n)), n))}