A190009 E.g.f.: exp(tan(x) + tan(x)^2).

1, 1, 3, 9, 49, 237, 1739, 11557, 105313, 886201, 9596211, 97408641, 1218112465, 14446293669, 204461028347, 2769624924637, 43702453433281, 664858164527089, 11560367630382051, 194954793455032569, 3700614762669466993, 68462595466239603165, 1407869708935659210155

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..468

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)) *binomial(m,k-m))/m!), n>0, a(0)=1.

Mathematica

With[{nmax = 50}, CoefficientList[Series[Exp[Tan[x] + Tan[x]^2], {x, 0, nmax}], x]*Range[0, nmax]!] (* G. C. Greubel, Jan 11 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)*binomial(m, k-m), k, m, n)/m!, m, 1, n);
(PARI) x='x+O('x^30); Vec(serlaplace(exp(tan(x)+tan(x)^2))) \\ G. C. Greubel, Jan 11 2018

Crossrefs

Sequence in context: A001530 A316449 A356270 * A012063 A036751 A260156

Adjacent sequences: A190006 A190007 A190008 * A190010 A190011 A190012

Keyword

nonn

Author

Vladimir Kruchinin, May 03 2011

Extensions

Terms a(18) onward added by G. C. Greubel, Jan 11 2018

Status

approved