A307874 - OEIS

%I #11 Jun 24 2022 07:57:56

%S 1,1,0,-1,4,-12,-3,640,-9721,107849,-766116,-5716810,438016259,

%T -13557651987,318299775147,-5284369281919,-5483686862123,

%U 6119663470743306,-388801742002632589,17841761552418336070,-645131407697518621805,14383670984970068901209,384858376828629625293001

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

%H Seiichi Manyama, <a href="/A307874/b307874.txt">Table of n, a(n) for n = 1..331</a>

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

%t 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]!]

%t a[n_] := a[n] = Sum[StirlingS1[n - 1, k] a[k], {k, 1, n - 1}]; a[1] = 1; Table[a[n], {n, 1, 23}]

%o (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

%Y Cf. A003659, A008275, A143805.

%K sign

%O 1,5

%A _Ilya Gutkovskiy_, May 02 2019