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Expansion of e.g.f. 1 / (1 + x * log(1 - x^4/24)).
2

%I #10 Aug 19 2024 12:14:50

%S 1,0,0,0,0,5,0,0,0,315,6300,0,0,150150,6306300,94594500,0,268017750,

%T 17689171500,549972423000,7332965640000,1283268987000,117632990475000,

%U 5681673439942500,155840185781280000,1961530116170625000,1606200062942475000

%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)!*abs(stirling(k, n-4*k, 1))/(24^k*k!));

%Y Cf. A052830, A375167, A375556.

%K nonn

%O 0,6

%A _Seiichi Manyama_, Aug 19 2024