A375167 Expansion of e.g.f. 1 / (1 + x * log(1 - x^2/2)).
1, 0, 0, 3, 0, 15, 180, 210, 5040, 51030, 207900, 3991680, 42411600, 356756400, 6485398920, 80635054500, 1040690851200, 19440077857200, 291313362740400, 4914773560897200, 98182334033784000, 1763213788027692000, 35636304386103220800, 778379605589616030000
Offset: 0
Keywords
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+x*log(1-x^2/2)))) -
PARI
a(n) = n!*sum(k=0, n\2, (n-2*k)!*abs(stirling(k, n-2*k, 1))/(2^k*k!));
Formula
a(n) = n! * Sum_{k=0..floor(n/2)} (n-2*k)! * |Stirling1(k,n-2*k)|/(2^k*k!).