A009390 Expansion of e.g.f.: log(1 + tanh(x))*exp(x).

0, 1, 1, 0, 0, 5, 5, -56, -56, 1329, 1329, -49192, -49192, 2653573, 2653573, -196707408, -196707408, 19194804737, 19194804737, -2385684870704, -2385684870704, 367985503366821, 367985503366821, -68980888889771080, -68980888889771080

Offset

0,6

Links

G. C. Greubel, Table of n, a(n) for n = 0..486

Formula

G.f.: x/(x^2-1)*(T(0)*(1+x)/(1+2*x) -2), where T(k) = 1 - x^2*(k+1)^2/(x^2*(k+1)^2 + (1+2*x)^2/T(k+1)); (continued fraction). - Sergei N. Gladkovskii, Nov 11 2013

a(n) = Sum_{k=0..floor((n-1)/2)} A028296(k). - Daniel Suteu, Nov 16 2018

a(n) = Sum_{k=0..n-1} E(k), where E(k) = A122045(k). - Amiram Eldar and Thomas Ordowski, Feb 06 2020

Maple

seq(add(euler(k), k=0..n-1), n=0..24); # Peter Luschny, Feb 06 2020

Mathematica

With[{nmax = 30}, CoefficientList[Series[Log[1 + Tanh[x]]*Exp[x], {x, 0, nmax}], x]*Range[0, nmax]!] (* G. C. Greubel, Nov 16 2018 *)

Prog

(PARI) a(n) = sum(k=0, floor((n-1)/2), 2*imag(polylog(-2*k, I))); \\ Daniel Suteu, Nov 16 2018
(PARI) x='x+O('x^30); concat([0], Vec(serlaplace(log(1+tanh(x))*exp(x)))) \\ G. C. Greubel, Nov 16 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Exp(x)*Log(1 + Tanh(x)))); [0] cat [Factorial(n)*b[n]: n in [1..(m-1)]]; // G. C. Greubel, Nov 16 2018

Crossrefs

Cf. A122045, A173226.

Sequence in context: A073128 A189749 A368894 * A009334 A151467 A241209

Adjacent sequences: A009387 A009388 A009389 * A009391 A009392 A009393

Keyword

sign,easy

Author

R. H. Hardin

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997

Status

approved