%I #25 Nov 19 2023 08:21:58

%S 1,4,16,68,316,1616,9080,55800,373080,2699520,21035040,175708320,

%T 1566916320,14862171840,149429426880,1587766126080,17779538050560,

%U 209295747832320,2583920845209600,33389139008678400,450642388471395840,6342869733912760320

%N Expansion of e.g.f. 1/(1 - log(1 + x))^4.

%C a(46) is negative. - _Vaclav Kotesovec_, Jun 04 2022

%C It appears that a(n) is negative for even n >= 46. - _Felix Fröhlich_, Jun 04 2022

%H Vaclav Kotesovec, <a href="/A354121/b354121.txt">Table of n, a(n) for n = 0..450</a>

%F a(n) = (1/6) * Sum_{k=0..n} (k + 3)! * Stirling1(n,k).

%F a(0) = 1; a(n) = Sum_{k=1..n} (-1)^(k-1) * (3 * k/n + 1) * (k-1)! * binomial(n,k) * a(n-k). - _Seiichi Manyama_, Nov 19 2023

%t Table[Sum[(k+3)! * StirlingS1[n,k], {k,0,n}]/6, {n,0,20}] (* _Vaclav Kotesovec_, Jun 04 2022 *)

%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-log(1+x))^4))

%o (PARI) a(n) = sum(k=0, n, (k+3)!*stirling(n, k, 1))/6;

%Y Cf. A006252, A317280, A354120.

%Y Cf. A226738, A354123.

%K sign

%O 0,2

%A _Seiichi Manyama_, May 17 2022