A353892 Expansion of e.g.f. exp( -(x * log(1-x))^3 / 36 ).

1, 0, 0, 0, 0, 0, 20, 210, 1960, 18900, 194880, 2166780, 26172080, 342599400, 4835694864, 73208215080, 1183011385920, 20318534134080, 369549843420384, 7094851788127680, 143377043010268800, 3042204544957939200, 67621161484919380800, 1571319471977711258880

Offset: 0

Author

Seiichi Manyama, May 09 2022

Keywords

• nonn

Crossrefs

Cf. A066166, A353891, A353893.

Cf. A347002, A353881, A353895.

Programs

PARI

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

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)!));

Formula

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