A191237 E.g.f. exp(x+x^3+x^5).

1, 1, 1, 7, 25, 181, 1201, 5251, 57457, 469225, 4340161, 50118751, 412902601, 5544552157, 69259632625, 816044592091, 12518563864801, 152563427413201, 2401979910598657, 39326158638385975, 575414895837696121

Offset: 0

Author

Vladimir Kruchinin, May 27 2011

Keywords

• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..125

Programs

Mathematica

a[n_] := n!*Sum[((-1)^(n - k) + 1)* Sum[ Binomial[j, (n - k)/2 - j]*Binomial[k, j], {j, 0, k}]/(2*k!), {k, 1, n}]; a[0] = 1; Table[a[n], {n, 0, 20}] (* Jean-François Alcover, Feb 21 2013 *)
With[{nn=20},CoefficientList[Series[Exp[x+x^3+x^5],{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Sep 21 2016 *)

Maxima

a(n):=n!*sum(((-1)^(n-k)+1)*sum(binomial(j,(n-k)/2-j)*binomial(k,j),j,0,k)/(2*k!),k,1,n);

PARI

x='x+O('x^66); /* that many terms */
Vec(serlaplace(exp(x+x^3+x^5))) /* show terms */ /* Joerg Arndt, May 28 2011 */

Formula

a(n)=n!*sum(k=1..n, ((-1)^(n-k)+1)*sum(binomial(j,(n-k)/2-j)*binomial(k,j),j,0,k)/(2*k!)), n>0, a(0)=1.