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A207654
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G.f.: Sum_{n>=0} Product_{k=1..n} ((1+x)^(2*k-1) - 1)/(1 - x^(2*k-1)).
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4
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1, 1, 4, 22, 173, 1816, 23659, 367573, 6622465, 135637477, 3111148862, 78984029782, 2198423489832, 66562555228478, 2177861372888738, 76571625673934064, 2878937040339348981, 115260759545001030638, 4895471242828376133806, 219853190410155476470763
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) ~ sqrt(6) * 24^n * n! / (exp(Pi^2/48) * sqrt(n) * Pi^(2*n+3/2)).
a(n) ~ 2^n * 12^(n+1/2) * n^n / (exp(n + Pi^2/48) * Pi^(2*n+1)).
(End)
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EXAMPLE
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G.f.: A(x) = 1 + x + 4*x^2 + 22*x^3 + 173*x^4 + 1816*x^5 + 23659*x^6 +...
such that, by definition,
A(x) = 1 + ((1+x)-1)/(1-x) + ((1+x)-1)*((1+x)^3-1)/((1-x)*(1-x^3)) + ((1+x)-1)*((1+x)^3-1)*((1+x)^5-1)/((1-x)*(1-x^3)*(1-x^5)) +...
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MATHEMATICA
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With[{nn=20}, CoefficientList[Series[Sum[Product[((1+x)^(2k-1)-1)/(1- x^(2k-1)), {k, n}], {n, 0, nn}], {x, 0, nn}], x]] (* Harvey P. Dale, Sep 06 2015 *)
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PROG
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(PARI) {a(n)=polcoeff(sum(m=0, n, prod(k=1, m, ((1+x)^(2*k-1)-1)/(1-x^(2*k-1) +x*O(x^n)) )), n)}
for(n=0, 25, print1(a(n), ", "))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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