A360482
E.g.f. satisfies A(x) = x * exp(x + 3 * A(x)).
Original entry on oeis.org
0, 1, 8, 120, 2848, 92960, 3868224, 195810496, 11680512512, 802445898240, 62396469222400, 5417515922441216, 519519435065020416, 54535504354085687296, 6219954774471102242816, 765903524713482618101760, 101269330068289021683564544, 14310318526812295078276628480
Offset: 0
-
my(N=20, x='x+O('x^N)); concat(0, Vec(serlaplace(-lambertw(-3*x*exp(x))/3)))
-
a(n) = sum(k=1, n, 3^(k-1)*k^(n-1)*binomial(n, k));
A360483
E.g.f. satisfies A(x) = x * exp(x - 2 * A(x)).
Original entry on oeis.org
0, 1, -2, 15, -172, 2685, -53226, 1281091, -36296408, 1183527225, -43660076950, 1797823266591, -81746462498724, 4068086310006901, -219929012455113794, 12835335232410655035, -804287930238495495856, 53858337558670992931185
Offset: 0
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my(N=20, x='x+O('x^N)); concat(0, Vec(serlaplace(lambertw(2*x*exp(x))/2)))
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a(n) = sum(k=1, n, (-2)^(k-1)*k^(n-1)*binomial(n, k));
A360484
E.g.f. satisfies A(x) = x * exp(x - 3 * A(x)).
Original entry on oeis.org
0, 1, -4, 48, -896, 22880, -743232, 29337280, -1363752448, 72979407360, -4419108684800, 298730433250304, -22300928914403328, 1822195561572585472, -161756111552270491648, 15501595224386724126720, -1595092357302221461127168, 175405731698165304882495488
Offset: 0
-
my(N=20, x='x+O('x^N)); concat(0, Vec(serlaplace(lambertw(3*x*exp(x))/3)))
-
a(n) = sum(k=1, n, (-3)^(k-1)*k^(n-1)*binomial(n, k));
A360471
E.g.f. satisfies A(x) = x * exp( 2*A(x) + x * exp(2*A(x)) ).
Original entry on oeis.org
0, 1, 6, 75, 1476, 39805, 1366278, 56998179, 2800588808, 158420939193, 10140538486410, 724652822705119, 57187947315670284, 4939834587311520117, 463572330418586227790, 46965096302630022564315, 5108915146530700018466832, 593925863391217441843199089
Offset: 0
Showing 1-4 of 4 results.