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%I #31 Oct 02 2021 07:57:29
%S 0,1,2,5,28,201,1566,14349,154456,1870225,25034650,368887573,
%T 5938767924,103580577881,1945112687350,39137964503837,840076566197552,
%U 19158967944112929,462642378426338994,11792392190823752229
%N Expansion of e.g.f. tan(x*exp(x)).
%H Seiichi Manyama, <a href="/A009635/b009635.txt">Table of n, a(n) for n = 0..100</a>
%F a(n) = 2*Sum_{m=0..floor((n-1)/2)} binomial(n, 2*m+1)*(2*m+1)^(n-2*m-1 * Sum_{j=1..2*m+1} j!*2^(2*m-j)*(-1)^(m+1+j)*Stirling2(2*m+1, j)). - _Vladimir Kruchinin_, Jun 10 2011
%t terms = 20;
%t egf = Tan[x*Exp[x]] + O[x]^terms ;
%t CoefficientList[egf, x] Range[0, terms - 1]! (* _Jean-François Alcover_, Sep 24 2019 *)
%o (Maxima)
%o a(n):=2*sum(binomial(n,2*m+1)*(2*m+1)^(n-2*m-1)*sum(j!*2^(2*m-j)*(-1)^(m+1+j)*stirling2(2*m+1,j),j,1,2*m+1),m,0,(n-1)/2); /* _Vladimir Kruchinin_, Jun 10 2011 */
%Y Cf. A009017, A009448, A009768, A191719.
%K nonn
%O 0,3
%A _R. H. Hardin_
%E Extended, reformatted, offset corrected 03/97.
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