A009737 Expansion of e.g.f. tan(x)*exp(tan(x)).

0, 1, 2, 5, 20, 81, 438, 2477, 16680, 120481, 973034, 8496245, 80252732, 817734321, 8859646110, 102873611549, 1258403748432, 16372688411713, 223202277906386, 3213260867586149, 48295209177888356

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..475

Formula

a(n) = Sum_{k=1..n} ( ((1+(-1)^(n-k))/(k-1)!) * Sum_{j=k..n} j! * Stirling2(n,j) * 2^(n-j-1)*(-1)^((n+k)/2+j)*binomial(j-1,k-1) ) ). - Vladimir Kruchinin, 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

Maple

m:= 30; S:= series(tan(x)*exp(tan(x)), x, m+1); seq(j!*coeff(S, x, j), j = 0..m); # G. C. Greubel, Mar 09 2021

Mathematica

With[{nn=20}, CoefficientList[Series[Tan[x]Exp[Tan[x]], {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Oct 30 2011 *)

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, Apr 19 2011]
(Sage)
[factorial(n)*( tan(x)*exp(tan(x)) ).series(x, n+1).list()[n] for n in (0..30)] # G. C. Greubel, Mar 09 2021
(Magma)
R<x>:=PowerSeriesRing(Rationals(), 30);
[0] cat Coefficients(R!( Laplace( Tan(x)*Exp(Tan(x)) ) )); // G. C. Greubel, Mar 09 2021

Crossrefs

Cf. A052852, A059419, A008277.

Sequence in context: A027041 A355866 A186767 * A280624 A008983 A286284

Adjacent sequences: A009734 A009735 A009736 * A009738 A009739 A009740

Keyword

nonn,easy

Author

R. H. Hardin

Extensions

Extended and signs tested by Olivier Gérard, Mar 15 1997

Status

approved