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Expansion of e.g.f. 1 / (1 - x * log(1 + x^4/24)).
1

%I #9 Aug 19 2024 12:14:47

%S 1,0,0,0,0,5,0,0,0,-315,6300,0,0,150150,-6306300,94594500,0,

%T -268017750,17689171500,-549972423000,7332965640000,1283268987000,

%U -117632990475000,5681673439942500,-155840185781280000,1934474528361375000,1606200062942475000

%N Expansion of e.g.f. 1 / (1 - x * log(1 + x^4/24)).

%F a(n) = n! * Sum_{k=0..floor(n/4)} (n-4*k)! * Stirling1(k,n-4*k)/(24^k*k!).

%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-x*log(1+x^4/24))))

%o (PARI) a(n) = n!*sum(k=0, n\4, (n-4*k)!*stirling(k, n-4*k, 1)/(24^k*k!));

%Y Cf. A375557.

%K sign

%O 0,6

%A _Seiichi Manyama_, Aug 19 2024