A226839 E.g.f.: exp( Sum_{n>=1} x^(n*(n+1)/2) / n! ).

1, 1, 1, 4, 13, 31, 271, 1576, 6049, 55693, 573661, 3839716, 36369301, 432793219, 3670898323, 47260464616, 758854978561, 8126729609401, 106290146259289, 1742497711849828, 22974498485218621, 454423040764317031, 8508721270142443351, 120131676428508219784, 2346431431552540513633

Offset: 0

Author

Paul D. Hanna, Jun 19 2013

Keywords

• nonn

Comments

E.g.f. may be written as: exp( Sum_{n>=1} Product_{k=1..n} x^k/k ).

Sum_{n>=0} a(n)/n! = e^(e-1) = 5.574941524760880...

Examples

			E.g.f.: A(x) = 1 + x + x^2/2! + 4*x^3/3! + 13*x^4/4! + 31*x^5/5! + 271*x^6/6! +...
where
log(A(x)) = x + x^3/2! + x^6/3! + x^10/4! + x^15/5! + x^21/6! + x^28/7! +...
		

Crossrefs

Cf. A226838.

Programs

PARI

{a(n)=n!*polcoeff(exp(sum(m=1,n,x^(m*(m+1)/2)/m!)+x*O(x^n)),n)}
for(n=0,30,print1(a(n),", "))

Formula

a(n) == 1 (mod 3) (conjecture - valid up to n=1024; if true for n>=0, why?).