A335986 E.g.f. A(x) satisfies: A'(x) = 1 + A(1 - exp(x)).

1, -1, -2, -2, 2, 12, 0, -190, -696, 1960, 29592, 49750, -1200226, -8200478, 51479530, 992408898, -517104450, -133585331394, -757952722052, 18448429372430, 284177581205280, -2033645276651570, -87779867499696610, -122540992214640738, 26825921931152034414

Offset

1,3

Links

Table of n, a(n) for n=1..25.

Formula

a(1) = 1; a(n) = Sum_{k=1..n-1} (-1)^k * Stirling2(n-1,k) * a(k).

Mathematica

terms = 25; A[_] = 0; Do[A[x_] = Normal[Integrate[1 + A[1 - Exp[x] + O[x]^(terms + 1)], x] + O[x]^(terms + 1)], terms]; CoefficientList[A[x], x] Range[0, terms]! // Rest
a[1] = 1; a[n_] := a[n] = Sum[(-1)^k StirlingS2[n - 1, k] a[k], {k, 1, n - 1}]; Table[a[n], {n, 1, 25}]

Crossrefs

Cf. A003659.

Sequence in context: A121223 A327559 A139518 * A096855 A152662 A135322

Adjacent sequences: A335983 A335984 A335985 * A335987 A335988 A335989

Keyword

sign

Author

Ilya Gutkovskiy, Jul 03 2020

Status

approved