A307874 E.g.f. A(x) satisfies: d/dx A(x) = 1 + A(log(1+x)).

1, 1, 0, -1, 4, -12, -3, 640, -9721, 107849, -766116, -5716810, 438016259, -13557651987, 318299775147, -5284369281919, -5483686862123, 6119663470743306, -388801742002632589, 17841761552418336070, -645131407697518621805, 14383670984970068901209, 384858376828629625293001

Offset

1,5

Links

Seiichi Manyama, Table of n, a(n) for n = 1..331

Formula

Recurrence: a(n+1) = Sum_{k=1..n} Stirling1(n,k) * a(k).

Mathematica

terms = 23; A[_] = 0; Do[A[x_] = Normal[Integrate[1 + A[Log[1 + x] + O[x]^(terms + 1)], x] + O[x]^(terms + 1)], terms]; Rest[CoefficientList[A[x], x] Range[0, terms]!]
a[n_] := a[n] = Sum[StirlingS1[n - 1, k] a[k], {k, 1, n - 1}]; a[1] = 1; Table[a[n], {n, 1, 23}]

Prog

(PARI) a_vector(n) = my(v=vector(n)); v[1]=1; for(i=1, n-1, v[i+1]=sum(j=1, i, stirling(i, j, 1)*v[j])); v; \\ Seiichi Manyama, Jun 24 2022

Crossrefs

Cf. A003659, A008275, A143805.

Sequence in context: A317555 A213343 A308518 * A230057 A205124 A224512

Adjacent sequences: A307871 A307872 A307873 * A307875 A307876 A307877

Keyword

sign

Author

Ilya Gutkovskiy, May 02 2019

Status

approved