A190010 E.g.f. exp(tan(x)+tan(x)^2+tan(x)^3).

1, 1, 3, 15, 73, 537, 3899, 35623, 345553, 3767185, 44993331, 575013087, 8040614041, 118459611753, 1883371991531, 31449522256183, 558550869727393, 10410156829764769, 204093418753532259, 4191381846930998319, 89889103856588434921

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..460

Formula

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.

Mathematica

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 *)

Prog

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

Crossrefs

Sequence in context: A007142 A357222 A224397 * A151326 A063000 A002902

Adjacent sequences: A190007 A190008 A190009 * A190011 A190012 A190013

Keyword

nonn

Author

Vladimir Kruchinin, May 03 2011

Status

approved