A360481
E.g.f. satisfies A(x) = x * exp(x + 2 * A(x)).
Original entry on oeis.org
0, 1, 6, 63, 1044, 23805, 692118, 24482115, 1020584232, 49000005945, 2662853279850, 161586078510879, 10830019921469532, 794577001293803637, 63339899145968483262, 5451312770064188283195, 503784284643602483767632, 49757423537114340032969073
Offset: 0
-
my(N=20, x='x+O('x^N)); concat(0, Vec(serlaplace(-lambertw(-2*x*exp(x))/2)))
-
a(n) = sum(k=1, n, 2^(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
-
my(N=20, x='x+O('x^N)); concat(0, Vec(serlaplace(lambertw(2*x*exp(x))/2)))
-
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));
A360545
E.g.f. satisfies A(x) = x * exp( 3*(x + A(x))/2 ).
Original entry on oeis.org
0, 1, 6, 54, 756, 14580, 358668, 10736712, 378823392, 15395255280, 708217959600, 36380741745744, 2064234271203360, 128214974795177088, 8652900673357097472, 630483717450225530880, 49330027417316557012992, 4124992361928178722764544
Offset: 0
-
my(N=20, x='x+O('x^N)); concat(0, Vec(serlaplace(-2*lambertw(-3*x/2*exp(3*x/2))/3)))
-
a(n) = sum(k=1, n, (3*k/2)^(n-1)*binomial(n, k));
Showing 1-4 of 4 results.