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E.g.f.: Sum_{n>=0} Product_{k=1..n} (exp((2*k-1)*x) - 1) / (2*k-1).
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%I #7 May 05 2014 03:54:30

%S 1,1,3,19,191,2731,52063,1264747,37912143,1368247627,58312623743,

%T 2889264152875,164299982895535,10607439707069323,770371122097072863,

%U 62438253016068932203,5608567981763102915087,554952834214350689736139,60161153106358242206145343

%N E.g.f.: Sum_{n>=0} Product_{k=1..n} (exp((2*k-1)*x) - 1) / (2*k-1).

%H Vaclav Kotesovec, <a href="/A218261/b218261.txt">Table of n, a(n) for n = 0..165</a>

%e E.g.f.: A(x) = 1 + x + 3*x^2/2! + 19*x^3/3! + 191*x^4/4! + 2731*x^5/5! +...

%e where

%e A(x) = 1 + (exp(x)-1) + (exp(x)-1)*(exp(3*x)-1)/(1*3) + (exp(x)-1)*(exp(3*x)-1)*(exp(5*x)-1)/(1*3*5) + (exp(x)-1)*(exp(3*x)-1)*(exp(5*x)-1)*(exp(7*x)-1)/(1*3*5*7) +...

%o (PARI) {a(n)=local(X=x+x*O(x^n),Egf);Egf=sum(m=0,n,prod(k=1,m,(exp((2*k-1)*X)-1)/(2*k-1)));n!*polcoeff(Egf,n)}

%o for(n=0,30,print1(a(n),", "))

%Y Cf. A215066, A135752.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Oct 24 2012