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A009737
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Expansion of tan(x)*exp(tan(x)).
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1
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0, 1, 2, 5, 20, 81, 438, 2477, 16680, 120481, 973034, 8496245, 80252732, 817734321, 8859646110, 102873611549, 1258403748432, 16372688411713, 223202277906386, 3213260867586149, 48295209177888356
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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FORMULA
| a(n):=sum(k=1..n, (1+(-1)^(n-k))*sum(j=k..n, j!*stirling2(n,j)*2^(n-j-1)*(-1)^((n+k)/2+j)*binomial(j-1,k-1))/(k-1)!). [Vladimir Kruchinin (kru(AT)ie.tusur.ru), Apr 19 2011]
a(n) = D^n(x*exp(x)) evaluated at x = 0, where D is the operator (1+x^2)*d/dx. Cf. A052852. a(n) = sum {k = 1..n} k*A059419(n,k). - Peter Bala, Nov 25 2011
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MATHEMATICA
| With[{nn=20}, CoefficientList[Series[Tan[x]Exp[Tan[x]], {x, 0, nn}], x] Range[0, nn]!] (* From Harvey P. Dale, Oct 30 2011 *)
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PROG
| (Maxima)
a(n):=sum((1+(-1)^(n-k))*sum(j!*stirling2(n, j)*2^(n-j-1)*(-1)^((n+k)/2+j)*binomial(j-1, k-1), j, k, n)/(k-1)!, k, 1, n); [Vladimir Kruchinin (kru(AT)ie.tusur.ru), Apr 19 2011]
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CROSSREFS
| Sequence in context: A189734 A027041 A186767 * A008983 A192101 A012768
Adjacent sequences: A009734 A009735 A009736 * A009738 A009739 A009740
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KEYWORD
| nonn,easy
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AUTHOR
| R. H. Hardin (rhhardin(AT)att.net)
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EXTENSIONS
| Extended and signs tested Mar 15 1997 by Olivier Gerard.
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