A335981 Expansion of e.g.f. exp(3 * (1 - exp(-x)) + x).

1, 4, 13, 31, 40, -23, -95, 490, 823, -8393, 3766, 174775, -658787, -2751404, 34033297, -55552037, -1170734432, 9362348365, 3277050925, -562286419646, 3848880970147, 8815342530739, -356804325202730, 2389771436686339, 8677476137729929, -302470260552857660

Offset

0,2

Links

Table of n, a(n) for n=0..25.

Formula

a(n) = exp(3) * (-1)^n * Sum_{k>=0} (-3)^k * (k - 1)^n / k!.

a(0) = 1; a(n) = a(n-1) + 3 * Sum_{k=0..n-1} (-1)^(n-k-1) * binomial(n-1,k) * a(k).

Mathematica

nmax = 25; CoefficientList[Series[Exp[3 (1 - Exp[-x]) + x], {x, 0, nmax}], x] Range[0, nmax]!
a[0] = 1; a[n_] := a[n] = a[n - 1] + 3 Sum[(-1)^(n - k - 1) Binomial[n - 1, k] a[k], {k, 0, n - 1}]; Table[a[n], {n, 0, 25}]

Crossrefs

Cf. A027710, A078940, A109747, A309084, A335868, A335980, A335982.

Sequence in context: A075880 A042487 A154753 * A191189 A106302 A158842

Adjacent sequences: A335978 A335979 A335980 * A335982 A335983 A335984

Keyword

sign

Author

Ilya Gutkovskiy, Jul 03 2020

Status

approved