A009434
Expansion of e.g.f: log(1+x)/cosh(tanh(x)).
Original entry on oeis.org
0, 1, -1, -1, 0, 69, -225, -1653, 3976, 187401, -965385, -14516745, 61266744, 3032650893, -21187300953, -491788726653, 2947006495920, 166337505847057, -1463633608132017, -46261934493321105, 358635306874354320
Offset: 0
-
R:=PowerSeriesRing(Rationals(), 30);
[0] cat Coefficients(R!(Laplace( Log(1+x)/Cosh(Tanh(x)) ))); // G. C. Greubel, Sep 06 2023
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With[{nn=20},CoefficientList[Series[Log[1+x]/Cosh[Tanh[x]],{x,0,nn}], x] Range[0,nn]!] (* Harvey P. Dale, Jun 19 2013 *)
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my(x='x+O('x^30)); concat([0],Vec(serlaplace(log(1+x)/cosh(tanh(x))))) \\ Joerg Arndt, Sep 06 2023
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def A009434_list(prec):
P. = PowerSeriesRing(QQ, prec)
return P( log(1+x)/cosh(tanh(x)) ).egf_to_ogf().list()
A009434_list(40) # G. C. Greubel, Sep 06 2023
Definition clarified and prior Mathematica program replaced by
Harvey P. Dale, Jun 19 2013
A009436
Expansion of e.g.f. log(1+x)/exp(sin(x)).
Original entry on oeis.org
0, 1, -3, 8, -20, 59, -261, 1665, -12368, 99945, -888961, 8802045, -96423788, 1154791637, -14982150197, 209295667833, -3133083877248, 50039962416625, -849332973526881, 15266142375582901, -289679348425382572
Offset: 0
-
R:=PowerSeriesRing(Rationals(), 30);
[0] cat Coefficients(R!(Laplace( Log(1+x)*Exp(-Sin(x)) ))); // G. C. Greubel, Sep 08 2023
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With[{m=30}, CoefficientList[Series[Log[1+x]/E^Sin[x], {x,0,m}], x]*Range[0,m]!] (* Vaclav Kotesovec, Jan 23 2015 *)
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def A009436_list(prec):
P. = PowerSeriesRing(QQ, prec)
return P( log(1+x)*exp(-sin(x)) ).egf_to_ogf().list()
A009436_list(31) # G. C. Greubel, Sep 08 2023
A302610
Expansion of e.g.f. -log(1 - x)*arcsinh(x).
Original entry on oeis.org
0, 0, 2, 3, 4, 20, 158, 819, 3624, 33984, 427482, 3819915, 29665260, 404822340, 6948032310, 88407058635, 991515848400, 17715286764000, 383952670412850, 6349179054589875, 93532380775766100, 2063197602667372500, 53913667654307868750, 1098018631195048591875
Offset: 0
-log(1 - x)*arcsinh(x) = 2*x^2/2! + 3*x^3/3! + 4*x^4/4! + 20*x^5/5! + 158*x^6/6! + 819*x^7/7! + 3624*x^8/8! + ...
Cf.
A009410,
A009416,
A009429,
A009435,
A012572,
A104150,
A177699,
A177700,
A296435,
A296727,
A302611.
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a:=series(-log(1-x)*arcsinh(x),x=0,24): seq(n!*coeff(a,x,n),n=0..23); # Paolo P. Lava, Mar 26 2019
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nmax = 23; CoefficientList[Series[-Log[1 - x] ArcSinh[x], {x, 0, nmax}], x] Range[0, nmax]!
A302611
Expansion of e.g.f. -log(1 - x)*arctanh(x).
Original entry on oeis.org
0, 0, 2, 3, 16, 50, 368, 1764, 16896, 109584, 1297152, 10628640, 149944320, 1486442880, 24349317120, 283465647360, 5287713177600, 70734282393600, 1480103564083200, 22376988058521600, 519000166327910400, 8752948036761600000, 222845873874075648000, 4148476779335454720000
Offset: 0
-log(1 - x)*arctanh(x) = 2*x^2/2! + 3*x^3/3! + 16*x^4/4! + 50*x^5/5! + 368*x^6/6! + 1764*x^7/7! + 16896*x^8/8! + ...
Cf.
A005359,
A009410,
A009416,
A009429,
A009435,
A012697,
A081358,
A104150,
A177699,
A177700,
A202139,
A302610.
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a:=series(-log(1-x)*arctanh(x),x=0,24): seq(n!*coeff(a,x,n),n=0..23); # Paolo P. Lava, Mar 26 2019
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nmax = 23; CoefficientList[Series[-Log[1 - x] ArcTanh[x], {x, 0, nmax}], x] Range[0, nmax]!
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x='x+O('x^99); concat([0, 0], Vec(serlaplace(log(1-x)*log((1-x)/(1+x))/2))) \\ Altug Alkan, Apr 10 2018
A351883
Expansion of e.g.f. 1 / (1 - x)^sech(x).
Original entry on oeis.org
1, 1, 2, 3, 6, 35, 285, 2044, 13804, 108093, 1083405, 12281896, 143452386, 1763156031, 23845410407, 353626471808, 5579871336488, 92609430408361, 1627509065584185, 30379312334903408, 598533509334403470, 12366674489588950555, 267527916985316556019
Offset: 0
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nmax = 22; CoefficientList[Series[1/(1 - x)^Sech[x], {x, 0, nmax}], x] Range[0, nmax]!
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my(x='x+O('x^30)); Vec(serlaplace(1/(1-x)^(1/cosh(x)))) \\ Michel Marcus, Feb 23 2022
Showing 1-5 of 5 results.