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E.g.f. exp(tan(x)+tan(x)^2+tan(x)^3).
1

%I #8 Jan 11 2018 03:13:04

%S 1,1,3,15,73,537,3899,35623,345553,3767185,44993331,575013087,

%T 8040614041,118459611753,1883371991531,31449522256183,558550869727393,

%U 10410156829764769,204093418753532259,4191381846930998319,89889103856588434921

%N E.g.f. exp(tan(x)+tan(x)^2+tan(x)^3).

%H G. C. Greubel, <a href="/A190010/b190010.txt">Table of n, a(n) for n = 0..460</a>

%F a(n) = Sum_{m=1..n} (Sum_{k=m..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)) *Sum_{j=0..m} binomial(j,-3*m+k+2*j) *binomial(m,j)))/m!), n>0, a(0)=1.

%t With[{nmax = 50}, CoefficientList[Series[Exp[Tan[x] + Tan[x]^2 + Tan[x]^3], {x, 0, nmax}], x]*Range[0, nmax]!] (* _G. C. Greubel_, Jan 10 2018 *)

%o (Maxima) a(n):=sum(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) *sum(binomial(j,-3*m+k+2*j) *binomial(m,j),j,0,m),k,m,n)/m!,m,1,n);

%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(tan(x)+tan(x)^2+tan(x)^3))) \\ _G. C. Greubel_, Jan 10 2018

%K nonn

%O 0,3

%A _Vladimir Kruchinin_, May 03 2011