A307135 E.g.f. A(x) satisfies: d/dx A(x) = 1 + A(x*exp(-x)).

1, 1, -1, -4, 28, -57, -1083, 21471, -227625, 5520, 86174720, -3173050975, 75628524701, -767388080795, -51335279965137, 4735502400094008, -256809556499479624, 9917182521618152375, -139386576755496491719, -23350708366359596018589, 3390048061391916232664831

Offset

1,4

Links

Table of n, a(n) for n=1..21.

Formula

Recurrence: a(n+1) = Sum_{k=1..n} binomial(n,k)*(-k)^(n-k)*a(k).

Mathematica

terms = 21; A[_] = 0; Do[A[x_] = Normal[Integrate[1 + A[x Exp[-x] + O[x]^(terms + 1)], x] + O[x]^(terms + 1)], terms]; Rest[CoefficientList[A[x], x] Range[0, terms]!]
a[n_] := a[n] = Sum[Binomial[n - 1, k] (-k)^(n - k - 1) a[k], {k, 1, n - 1}]; a[1] = 1; Table[a[n], {n, 1, 21}]

Crossrefs

Cf. A003659, A193162.

Sequence in context: A061428 A069518 A151912 * A101002 A197542 A203280

Adjacent sequences: A307132 A307133 A307134 * A307136 A307137 A307138

Keyword

sign

Author

Ilya Gutkovskiy, May 04 2019

Status

approved