A003723 E.g.f. exp(tanh(x)).

1, 1, 1, -1, -7, -3, 97, 275, -2063, -15015, 53409, 968167, -752343, -77000363, -166831871, 7433044411, 43685848289, -843598411471, -9398558916159, 107426835190735, 2116926930779225, -14072980460605907

Offset: 0

Author

R. H. Hardin, Simon Plouffe

Keywords

• sign

Comments

Row sums of triangle A111593.

References

• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• T. D. Noe, Table of n, a(n) for n = 0..100

Crossrefs

Cf. A003706, A003710.

Programs

Mathematica

With[{nn = 30}, CoefficientList[Series[Exp[Tanh[x]], {x, 0, nn}], x] Range[0, nn]!] (* Vincenzo Librandi, Apr 11 2014 *)

Maxima

a(n):=if n=0 then 1 else sum(sum(binomial(k-1,m-1)*k!*(-1)^(m+k)*2^(n-k)*stirling2(n,k),k,m,n)/m!,m,1,n); /* Vladimir Kruchinin, Jun 28 2011 */

Formula

a(n) := sum(m=1..n, sum(k=m..n, binomial(k-1,m-1)*k!*(-1)^(m+k)*2^(n-k)*Stirling2(n,k))/m!), n>0, a(0)=1. - Vladimir Kruchinin, Jun 28 2011