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%I #6 Mar 12 2022 13:13:41
%S 1,1,7,100,2438,90246,4702142,327233880,29271020760,3268118467608,
%T 445031112068232,72541135526581536,13936782476047959024,
%U 3115165518696599108976,801181037747755210248432,234835083029394312036638016,77797056535321496989078410624
%N E.g.f.: exp( Sum_{n>=1} x^n * Sum_{k=1..n} 1/k^2 ) = Sum_{n>=0} a(n)*x^n/n!^2.
%e E.g.f.: A(x) = 1 + x + 7*x^2/2!^2 + 100*x^3/3!^2 + 2438*x^4/4!^2 + 90246*x^5/5!^2 +...
%e such that
%e log(A(x)) = x + x^2*(1+1/4) + x^3*(1+1/4+1/9) + x^4*(1+1/4+1/9+1/16) + x^5*(1+1/4+1/9+1/16+1/25) + x^6*(1+1/4+1/9+1/16+1/25+1/36) +...
%o (PARI) {a(n)=n!^2*polcoeff(exp(sum(m=1, n+1, x^m*sum(k=1, m, 1/k^2)+x*O(x^n))), n)}
%o for(n=0,20,print1(a(n),", "))
%Y Cf. A087761.
%K nonn
%O 0,3
%A _Paul D. Hanna_, May 03 2012
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