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A003704 Expansion of log(1+sinh(x)).
(Formerly M2867)
4
0, 1, -1, 3, -10, 45, -256, 1743, -13840, 125625, -1282816, 14554683, -181649920, 2473184805, -36478744576, 579439207623, -9861412096000, 179018972217585, -3452931391553536, 70518070842040563, -1520176422094766080 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

REFERENCES

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

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

FORMULA

a(n) = sum(k=1..n, sum(i=0..k, (-1)^(n+i-1)*(k-2*i)^n * binomial(k,i)) /(k*2^k)). [Vladimir Kruchinin, Apr 20 2011]

a(n) ~ (-1)^(n+1) * (n-1)! / (log(1+sqrt(2)))^n. - Vaclav Kotesovec, Feb 16 2015

MATHEMATICA

With[{nn = 201}, CoefficientList[Series[Log[1 + Sinh[x]], {x, 0, nn}], x] Range[0, nn]!] (* Vincenzo Librandi, Apr 11 2014 *)

PROG

(Maxima)

a(n):=sum(sum((-1)^(n+i-1)*(k-2*i)^n*binomial(k, i), i, 0, k)/(k*2^k), k, 1, n); /* Vladimir Kruchinin, Apr 20 2011 */

CROSSREFS

Cf. A009344, A024293, A080795.

Sequence in context: A020026 A077002 A268224 * A236409 A000250 A118601

Adjacent sequences:  A003701 A003702 A003703 * A003705 A003706 A003707

KEYWORD

sign

AUTHOR

R. H. Hardin, Simon Plouffe

EXTENSIONS

Mathematica code replaced by Vincenzo Librandi, Apr 11 2014

STATUS

approved

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Last modified December 9 04:21 EST 2016. Contains 278960 sequences.