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 A009403 Expansion of e.g.f. log(1 + tanh(x)^2), even powers only. 2
 0, 2, -28, 992, -69088, 8110592, -1448424448, 366436769792, -124760831684608, 55014520738414592, -30501848618302701568, 20768078187214502100992, -17035983844637174375907328, 16570619538920401323784404992 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..100 FORMULA a(n) ~ (-1)^(n+1) * 2^(4*n) * (2*n)! / (n * Pi^(2*n)). - Vaclav Kotesovec, Apr 20 2014 From G. C. Greubel, Jul 12 2022: (Start) a(n) = 2*A024299(n). a(n) = -4^n * (4^n - 2)*(4^n - 1)*Zeta(1-2*n), with a(0) = 0. (End) MATHEMATICA With[{nn=30}, Take[CoefficientList[Series[Log[1+Tanh[x]^2], {x, 0, nn}], x] Range[0, nn]!, {1, -1, 2}]] (* Harvey P. Dale, Aug 27 2013 *) PROG (Magma) L:=RiemannZeta(); [0] cat [-Round(4^n*(4^n-2)*(4^n-1)*Evaluate(L, 1-2*n)): n in [1..20]]; // G. C. Greubel, Jul 12 2022 (SageMath) [0]+[-4^n*(4^n-2)*(4^n-1)*zeta(1-2*n) for n in (1..20)] # G. C. Greubel, Jul 12 2022 CROSSREFS Cf. A024299. Sequence in context: A264637 A352251 A012756 * A026944 A296464 A292806 Adjacent sequences: A009400 A009401 A009402 * A009404 A009405 A009406 KEYWORD sign AUTHOR EXTENSIONS Extended with signs by Olivier Gérard, Mar 15 1997 Previous Mathematica program replaced by Harvey P. Dale, Aug 27 2013 STATUS approved

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Last modified February 6 01:28 EST 2023. Contains 360091 sequences. (Running on oeis4.)