A003723 E.g.f. exp(tanh(x)). (Formerly M4327)

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

Offset

0,5

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

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

Mathematica

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

Prog

(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 */

Crossrefs

Cf. A003706, A003710.

Sequence in context: A372617 A183421 A173443 * A241438 A054471 A086453

Adjacent sequences: A003720 A003721 A003722 * A003724 A003725 A003726

Keyword

sign

Author

R. H. Hardin, Simon Plouffe

Status

approved