A331608
E.g.f.: exp(1 / (1 - sinh(x)) - 1).
Original entry on oeis.org
1, 1, 3, 14, 85, 632, 5559, 56352, 645929, 8252352, 116189291, 1786361216, 29764770941, 534082233856, 10264484355103, 210312181051392, 4575364233983057, 105310034714202112, 2556360647841415379, 65261358332774277120, 1747713179543456515749
Offset: 0
-
nmax = 20; CoefficientList[Series[Exp[1/(1 - Sinh[x]) - 1], {x, 0, nmax}], x] Range[0, nmax]!
A006154[n_] := Sum[Sum[(-1)^j (k - 2 j)^n Binomial[k, j]/2^k, {j, 0, k}], {k, 1, n}]; a[0] = 1; a[n_] := a[n] = Sum[Binomial[n - 1, k - 1] A006154[k] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 20}]
A331610
Expansion of e.g.f.: exp(1 / (1 - tan(x)) - 1).
Original entry on oeis.org
1, 1, 3, 15, 97, 777, 7379, 80983, 1007137, 13986289, 214383171, 3593224767, 65347120705, 1281151315641, 26928292883795, 603928982033863, 14392387319349697, 363135896514611041, 9669298448057196291, 270932711729869233903, 7967970654277850949025
Offset: 0
-
S:= series(exp(1/(1-tan(x))-1), x, 31):
seq(coeff(S,x,i)*i!, i=0..30); # Robert Israel, Dec 10 2024
-
nmax = 20; CoefficientList[Series[Exp[1/(1 - Tan[x]) - 1], {x, 0, nmax}], x] Range[0, nmax]!
A000111[n_] := If[EvenQ[n], Abs[EulerE[n]], Abs[(2^(n + 1) (2^(n + 1) - 1) BernoulliB[n + 1])/(n + 1)]]; a[0] = 1; a[n_] := a[n] = Sum[Binomial[n - 1, k - 1] 2^(k - 1) A000111[k] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 20}]
A331616
E.g.f.: exp(1 / (1 - arcsinh(x)) - 1).
Original entry on oeis.org
1, 1, 3, 12, 61, 380, 2783, 23240, 217817, 2267472, 25924827, 322257408, 4325450325, 62374428480, 961296291447, 15754664717184, 273537984529713, 5016337928401152, 96871316157146163, 1964030207217042432, 41706446669511523821, 925774982414999202816
Offset: 0
-
nmax = 21; CoefficientList[Series[Exp[1/(1 - ArcSinh[x]) - 1], {x, 0, nmax}], x] Range[0, nmax]!
A296675[0] = 1; A296675[n_] := A296675[n] = Sum[Binomial[n, k] If[OddQ[k], (-1)^Boole[IntegerQ[(k + 1)/4]] ((k - 2)!!)^2, 0] A296675[n - k], {k, 1, n}]; a[0] = 1; a[n_] := a[n] = Sum[Binomial[n - 1, k - 1] A296675[k] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 21}]
-
seq(n)={Vec(serlaplace(exp(1/(1 - asinh(x + O(x*x^n))) - 1)))} \\ Andrew Howroyd, Jan 22 2020
A331615
E.g.f.: exp(1 / (1 - arcsin(x)) - 1).
Original entry on oeis.org
1, 1, 3, 14, 85, 640, 5703, 58760, 685353, 8925632, 128231627, 2014061568, 34312150525, 630043097216, 12400033125647, 260357810321664, 5807790344591953, 137144754146230272, 3417248676737769619, 89590823377278496768, 2465026658283881339301
Offset: 0
-
nmax = 20; CoefficientList[Series[Exp[1/(1 - ArcSin[x]) - 1], {x, 0, nmax}], x] Range[0, nmax]!
A189780[0] = 1; A189780[n_] := A189780[n] = Sum[Binomial[n, k] If[OddQ[k], ((k - 2)!!)^2, 0] A189780[n - k], {k, 1, n}]; a[0] = 1; a[n_] := a[n] = Sum[Binomial[n - 1, k - 1] A189780[k] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 20}]
-
seq(n)={Vec(serlaplace(exp(1/(1 - asin(x + O(x*x^n))) - 1)))} \\ Andrew Howroyd, Jan 22 2020
Showing 1-4 of 4 results.
Comments