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Expansion of e.g.f. exp( -(x * log(1-x))^3 / 36 ).
3

%I #11 May 10 2022 11:41:02

%S 1,0,0,0,0,0,20,210,1960,18900,194880,2166780,26172080,342599400,

%T 4835694864,73208215080,1183011385920,20318534134080,369549843420384,

%U 7094851788127680,143377043010268800,3042204544957939200,67621161484919380800,1571319471977711258880

%N Expansion of e.g.f. exp( -(x * log(1-x))^3 / 36 ).

%F a(n) = n! * Sum_{k=0..floor(n/6)} (3*k)! * |Stirling1(n-3*k,3*k)|/(36^k * k! * (n-3*k)!).

%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(-(x*log(1-x))^3/36)))

%o (PARI) a(n) = n!*sum(k=0, n\6, (3*k)!*abs(stirling(n-3*k, 3*k, 1))/(36^k*k!*(n-3*k)!));

%Y Cf. A066166, A353891, A353893.

%Y Cf. A347002, A353881, A353895.

%K nonn

%O 0,7

%A _Seiichi Manyama_, May 09 2022