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A115327
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E.g.f.: exp(x + 3/2*x^2).
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7
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1, 1, 4, 10, 46, 166, 856, 3844, 21820, 114076, 703216, 4125496, 27331624, 175849480, 1241782816, 8627460976, 64507687696, 478625814544, 3768517887040, 29614311872416, 244419831433696, 2021278543778656, 17419727924101504
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OFFSET
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0,3
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COMMENTS
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Term-by-term square of sequence with e.g.f.: exp(x+m/2*x^2) is given by e.g.f.: exp(x/(1-m*x))/sqrt(1-m^2*x^2) for all m.
a(n) is also the number of square roots of any permutation in S_{3n} whose disjoint cycle decomposition consists of n cycles of length 3. - Luis Manuel Rivera Martínez, Feb 26 2015
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LINKS
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FORMULA
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Term-by-term square equals A115328 which has e.g.f.: exp(x/(1-3*x))/sqrt(1-9*x^2).
G.f.: 1/(1-x-3*x^2/(1-x-6*x^2/(1-x-9*x^2/(1-x-12*x^2/(1-... (continued fraction);
a(n) = a(n-1)+3*(n-1)*a(n-2). (End)
a(n) ~ exp(sqrt(n/3)-n/2-1/12)*3^(n/2)*n^(n/2)/sqrt(2). - Vaclav Kotesovec, Oct 19 2012
G.f.: 1/Q(0), where Q(k)= 1 + 3*x*k - x/(1 - 3*x*(k+1)/Q(k+1)); (continued fraction). - Sergei N. Gladkovskii, Apr 17 2013
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MATHEMATICA
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Range[0, 20]! CoefficientList[Series[Exp[(x + 3 / 2 x^2)], {x, 0, 20}], x] (* Vincenzo Librandi, May 22 2013 *)
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PROG
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(PARI) a(n)=local(m=3); n!*polcoeff(exp(x+m/2*x^2+x*O(x^n)), 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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