A189239 E.g.f. exp(x/cos(x)*exp(x/cos(x)))

1, 1, 3, 13, 77, 521, 4237, 38879, 402537, 4605697, 57796601, 787755255, 11583272461, 182651526513, 3072748617317, 54914056549231, 1038486405418449, 20713226786502529, 434426374539131761, 9555736871169618407, 219912659890141260661, 5283756963089094382705

Offset

0,3

Links

Table of n, a(n) for n=0..21.

Formula

a(n) = n! * sum(r=1..n, ((sum(k=r..n-1, (((-1)^(n-k)+1) * (sum(m=1..n-k, binomial(m+k-1,k-1) * sum(j=1..m, ((sum(i=0..floor((j-1)/2, (j-2*i)^(n-k) * binomial(j,i)))) * binomial(m,j) * (-1)^((n-k)/2-j))/2^j))) * r^(k-r))/((n-k)!*(k-r)!)))+r^(n-r)/(n-r)!)/r!);

Mathematica

With[{nn=30}, CoefficientList[Series[Exp[x/Cos[x] Exp[x/Cos[x]]], {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Aug 08 2015 *)

Prog

(Maxima)
a(n):=n!*sum(((sum((((-1)^(n-k)+1)*(sum(binomial(m+k-1, k-1)*sum(((sum((j-2*i)^(n-k)*binomial(j, i), i, 0, floor((j-1)/2)))*binomial(m, j)*(-1)^((n-k)/2-j))/2^j, j, 1, m), m, 1, n-k))*r^(k-r))/((n-k)!*(k-r)!), k, r, n-1))+r^(n-r)/(n-r)!)/r!, r, 1, n);
(PARI) x='x+O('x^66); /* that many terms */
egf=exp(x/cos(x)*exp(x/cos(x))); /* = 1 + x + 3/2*x^2 + 13/6*x^3 +... */
Vec(serlaplace(egf)) /* show terms */ /* Joerg Arndt, Apr 21 2011 */

Crossrefs

Sequence in context: A220895 A352308 A336421 * A074530 A159662 A032035

Adjacent sequences: A189236 A189237 A189238 * A189240 A189241 A189242

Keyword

nonn

Author

Vladimir Kruchinin, Apr 19 2011

Status

approved