A193435 exp( Sum_{n>=1} x^n / (n*(n+1)/2) ) = Sum_{n>=0} a(n)*x^n / (n!*(n+1)!).

1, 2, 10, 96, 1528, 36720, 1248560, 57272320, 3417283968, 257711328000, 23999961081600, 2707648512307200, 364172045286804480, 57600985355595601920, 10589369533424230348800, 2239779182794304126976000, 540207965396186411279155200

Offset: 0

Author

Paul D. Hanna, Jul 25 2011

Keywords

• nonn

Comments

Sum_{n>=0} a(n)/(n!*(n+1)!) = exp(2) = 7.389056098930...

Examples

			A(x) = 1 + 2*x/(1!*2!) + 10*x^2/(2!*3!) + 96*x^3/(3!*4!) + 1528*x^4/(4!*5!) +...
where
log(A(x)) = x + x^2/3 + x^3/6 + x^4/10 + x^5/15 + x^6/21 + x^7/28 +...
		

Crossrefs

Cf. A193436.

Programs

PARI

{a(n)=n!*(n+1)!*polcoeff(exp(sum(m=1,n,x^m/(m*(m+1)/2))+x*O(x^n)),n)}