A335982 Expansion of e.g.f. exp(4 * (1 - exp(-x)) + x).

1, 5, 21, 69, 149, 69, -619, -187, 9365, -3515, -193643, 453957, 4704917, -29425595, -83918443, 1640246085, -3184430955, -74516517307, 604223657877, 1324972362053, -52526078298475, 264984579390533, 2477371363954069, -44206576595187899, 133280843118435477

Offset

0,2

Links

Table of n, a(n) for n=0..24.

Formula

a(n) = exp(4) * (-1)^n * Sum_{k>=0} (-4)^k * (k - 1)^n / k!.

a(0) = 1; a(n) = a(n-1) + 4 * Sum_{k=0..n-1} (-1)^(n-k-1) * binomial(n-1,k) * a(k).

Mathematica

nmax = 24; CoefficientList[Series[Exp[4 (1 - Exp[-x]) + x], {x, 0, nmax}], x] Range[0, nmax]!
a[0] = 1; a[n_] := a[n] = a[n - 1] + 4 Sum[(-1)^(n - k - 1) Binomial[n - 1, k] a[k], {k, 0, n - 1}]; Table[a[n], {n, 0, 24}]

Crossrefs

Cf. A078944, A078945, A109747, A309085, A335868, A335980, A335981.

Sequence in context: A272310 A273740 A147246 * A271282 A203287 A296720

Adjacent sequences: A335979 A335980 A335981 * A335983 A335984 A335985

Keyword

sign

Author

Ilya Gutkovskiy, Jul 03 2020

Status

approved