A277473
E.g.f.: -exp(x)*LambertW(-x).
Original entry on oeis.org
0, 1, 4, 18, 116, 1060, 12702, 187810, 3296120, 66897288, 1540762010, 39693752494, 1130866726596, 35300006582620, 1198036854980630, 43921652697277170, 1729775120233353968, 72831210167041246480, 3264674481128340280242, 155220967397580333229270
Offset: 0
-
CoefficientList[Series[-Exp[x]*LambertW[-x], {x, 0, 20}], x] * Range[0, 20]!
Table[Sum[Binomial[n, k]*k^(k-1), {k, 1, n}], {n, 0, 20}]
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x='x+O('x^50); concat([0], Vec(serlaplace(-exp(x)*lambertw(-x)))) \\ G. C. Greubel, Jun 11 2017
A277485
E.g.f.: -exp(2*x)*LambertW(-x).
Original entry on oeis.org
0, 1, 6, 33, 216, 1865, 21228, 303765, 5222864, 104540337, 2383558740, 60933722069, 1725392415288, 53590463856345, 1811281159509500, 66172416761172885, 2598298697830360992, 109116931783034360801, 4880122696811960470692, 231565260558289051906965
Offset: 0
-
CoefficientList[Series[-Exp[2*x]*LambertW[-x], {x, 0, 20}], x]*Range[0, 20]!
Table[Sum[Binomial[n, m]*Sum[Binomial[m, k]*k^(k-1), {k, 1, m}], {m, 1, n}], {n, 0, 20}]
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x='x+O('x^50); concat([0], Vec(serlaplace(- exp(2*x)*lambertw(-x) ))) \\ G. C. Greubel, Nov 08 2017
A290215
a(n) = n! * [x^n] -exp(-n*x)*LambertW(-x).
Original entry on oeis.org
0, 1, -2, 18, -144, 1900, -26820, 485394, -9679936, 225394488, -5765768100, 164923889350, -5132384691984, 174433050454260, -6385752833589220, 251596880714336850, -10585338808667808000, 474507594337155230704, -22550580127644413987268
Offset: 0
-
Table[n! SeriesCoefficient[-Exp[-n x] LambertW[-x], {x, 0, n}], {n, 0, 18}]
Table[Sum[(-n)^(n - k) Binomial[n, k] k^(k - 1), {k, 1, n}], {n, 0, 18}]
Showing 1-3 of 3 results.
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