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A003723 E.g.f. exp(tanh(x)).
(Formerly M4327)
6
1, 1, 1, -1, -7, -3, 97, 275, -2063, -15015, 53409, 968167, -752343, -77000363, -166831871, 7433044411, 43685848289, -843598411471, -9398558916159, 107426835190735, 2116926930779225, -14072980460605907 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A248279 A183421 A173443 * A241438 A054471 A086453
KEYWORD
sign
AUTHOR
STATUS
approved

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Last modified March 28 20:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)