A291979
a(n) = (-1)^n*n!*[x^n] exp(-x)/(1 + log(1+x)).
Original entry on oeis.org
1, 2, 6, 27, 167, 1310, 12394, 137053, 1733325, 24670114, 390204086, 6789564639, 128884276179, 2650516064222, 58701784670138, 1392959655437473, 35257885037803417, 948208649740610466, 27000743345935785670, 811575543670852269347, 25677856392014665436799
Offset: 0
-
a_list := proc(n) exp(-x)/(1 + log(1+x)): series(%, x, n+1):
seq((-1)^k*k!*coeff(%, x, k), k=0..n) end: a_list(20);
-
nmax = 20; CoefficientList[Series[E^(-x)/(1 + Log[1+x]), {x, 0, nmax}], x] * Range[0, nmax]! * (-1)^Range[0, nmax] (* Vaclav Kotesovec, Sep 18 2017 *)
-
N=20; x='x+O('x^N); Vec(serlaplace(exp(x)/(1+log(1-x)))) \\ Seiichi Manyama, Oct 20 2021
A343709
a(n) = 1 + 3 * Sum_{k=0..n-1} binomial(n,k) * (n-k-1)! * a(k).
Original entry on oeis.org
1, 4, 28, 295, 4159, 73348, 1552468, 38336569, 1081926157, 34350646636, 1211796777748, 47023762576987, 1990643657768683, 91291802205304972, 4508735102829489580, 238583762726054522989, 13466532093135977880025, 807606110028529741369396, 51282242176105846536128236
Offset: 0
-
a[n_] := a[n] = 1 + 3 Sum[Binomial[n, k] (n - k - 1)! a[k], {k, 0, n - 1}]; Table[a[n], {n, 0, 18}]
nmax = 18; CoefficientList[Series[Exp[x]/(1 + 3 Log[1 - x]), {x, 0, nmax}], x] Range[0, nmax]!
-
N=20; x='x+O('x^N); Vec(serlaplace(exp(x)/(1+3*log(1-x)))) \\ Seiichi Manyama, Oct 20 2021
A343710
a(n) = 1 + 4 * Sum_{k=0..n-1} binomial(n,k) * (n-k-1)! * a(k).
Original entry on oeis.org
1, 5, 45, 609, 11009, 248837, 6749629, 213596401, 7725031521, 314310704101, 14209394894765, 706617979262049, 38333841625642785, 2252901018519028901, 142589176837851349757, 9669282207517755852721, 699408060608904410296897, 53752166013267632536864581, 4374061543586452325644329133
Offset: 0
-
a[n_] := a[n] = 1 + 4 Sum[Binomial[n, k] (n - k - 1)! a[k], {k, 0, n - 1}]; Table[a[n], {n, 0, 18}]
nmax = 18; CoefficientList[Series[Exp[x]/(1 + 4 Log[1 - x]), {x, 0, nmax}], x] Range[0, nmax]!
-
N=20; x='x+O('x^N); Vec(serlaplace(exp(x)/(1+4*log(1-x)))) \\ Seiichi Manyama, Oct 20 2021
A368285
Expansion of e.g.f. exp(2*x) / (1 + 2*log(1 - x)).
Original entry on oeis.org
1, 4, 22, 168, 1700, 21560, 328576, 5844608, 118827264, 2717955776, 69076424384, 1931128212992, 58895387322240, 1945869352171264, 69235812945551872, 2639436090012161024, 107329778640349652992, 4637225944423696109568, 212138681191492565180416
Offset: 0
-
a_vector(n) = my(v=vector(n+1)); for(i=0, n, v[i+1]=2^i+2*sum(j=1, i, (j-1)!*binomial(i, j)*v[i-j+1])); v;
A368286
Expansion of e.g.f. exp(-x) / (1 + 2*log(1 - x)).
Original entry on oeis.org
1, 1, 7, 51, 521, 6617, 100903, 1795091, 36497601, 834825089, 21217022903, 593152248323, 18089914384425, 597680325734905, 21266014041519799, 810711731123810051, 32966705053762073665, 1424339658492670445121, 65159114638457033834791
Offset: 0
-
a_vector(n) = my(v=vector(n+1)); for(i=0, n, v[i+1]=(-1)^i+2*sum(j=1, i, (j-1)!*binomial(i, j)*v[i-j+1])); v;
A368287
Expansion of e.g.f. exp(-2*x) / (1 + 2*log(1 - x)).
Original entry on oeis.org
1, 0, 6, 32, 356, 4456, 68096, 1211136, 24625408, 563266240, 14315378880, 400206928128, 12205482237824, 403262088466688, 14348434923733504, 546996936260529152, 22243031618999642112, 961019064912965103616, 43963636798214215278592
Offset: 0
-
a_vector(n) = my(v=vector(n+1)); for(i=0, n, v[i+1]=(-2)^i+2*sum(j=1, i, (j-1)!*binomial(i, j)*v[i-j+1])); v;
A368444
Expansion of e.g.f. exp(x) / (1 + log(1 - 2*x)).
Original entry on oeis.org
1, 3, 17, 155, 1937, 30499, 577793, 12784155, 323427041, 9207390211, 291277318065, 10136705490779, 384848820035057, 15829002092015267, 701141988610115617, 33275461169171553371, 1684504951149122303169, 90604594879948059236099
Offset: 0
-
a_vector(n) = my(v=vector(n+1)); for(i=0, n, v[i+1]=1+sum(j=1, i, 2^j*(j-1)!*binomial(i, j)*v[i-j+1])); v;
Showing 1-7 of 7 results.
Comments