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%I #11 Jun 19 2013 23:19:27
%S 1,1,1,4,13,31,271,1576,6049,55693,573661,3839716,36369301,432793219,
%T 3670898323,47260464616,758854978561,8126729609401,106290146259289,
%U 1742497711849828,22974498485218621,454423040764317031,8508721270142443351,120131676428508219784,2346431431552540513633
%N E.g.f.: exp( Sum_{n>=1} x^(n*(n+1)/2) / n! ).
%C E.g.f. may be written as: exp( Sum_{n>=1} Product_{k=1..n} x^k/k ).
%C Sum_{n>=0} a(n)/n! = e^(e-1) = 5.574941524760880...
%F a(n) == 1 (mod 3) (conjecture - valid up to n=1024; if true for n>=0, why?).
%e 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! +...
%e where
%e log(A(x)) = x + x^3/2! + x^6/3! + x^10/4! + x^15/5! + x^21/6! + x^28/7! +...
%o (PARI) {a(n)=n!*polcoeff(exp(sum(m=1,n,x^(m*(m+1)/2)/m!)+x*O(x^n)),n)}
%o for(n=0,30,print1(a(n),", "))
%Y Cf. A226838.
%K nonn
%O 0,4
%A _Paul D. Hanna_, Jun 19 2013
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