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%I
%S 1,1,3,12,66,449,3678,35111,383192,4704300,64172052,962908056,
%T 15762088585,279514500434,5338014558032,109224066408835,
%U 2383887010044728,55281768382909480,1357381019671809552,35180557115610914376,959798458208463538416,27494554196938752676656
%N E.g.f.: 1/(1 + Sum_{n>=1} (-1)^n*x^(n*(3*n-1)/2)/(n*(3*n-1)/2)! + (-1)^n*x^(n*(3*n+1)/2)/(n*(3*n+1)/2)! ).
%F a(n) is odd iff n is a generalized pentagonal number (A001318).
%e E.g.f.: A(x) = 1 + x + 3*x^2/2! + 12*x^3/3! + 66*x^4/4! + 449*x^5/5! + 3678*x^6/6! +...
%e where the reciprocal involves generalized pentagonal factorials:
%e A(x) = 1/(1 - x - x^2/2! + x^5/5! + x^7/7! - x^12/12! - x^15/15! + x^22/22! + x^26/26! - x^35/35! - x^40/40! +...).
%o (PARI) {a(n)=n!*polcoeff(1/(1+sum(m=1,n,(-1)^m*x^(m*(3*m-1)/2)/(m*(3*m-1)/2)!+(-1)^m*x^(m*(3*m+1)/2)/(m*(3*m+1)/2)! +x*O(x^n))),n)}
%Y Cf. A001318.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Nov 09 2011
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