OFFSET
0,3
FORMULA
a(n) = Sum_{k=0..n} |Stirling1(n,k)|*A000085(k).
From Emanuele Munarini, Jul 09 2022: (Start)
a(n) = Sum_{k=0..n/2} |Stirling1(n+1,2*k+1)|*binomial(2*k,k)*k!/2^k.
a(n+1) = (n+1)*a(n) - Sum_{k=1..n} binomial(n,k)*(k-1)!*a(n-k). (End)
MAPLE
seq(n!*coeff(series(exp(log(1-x)^2/2)/(1-x), x=0, 23), x, n), n=0..22); # Paolo P. Lava, Jan 28 2019
MATHEMATICA
nmax = 22; CoefficientList[Series[Exp[Log[1 - x]^2/2]/(1 - x), {x, 0, nmax}], x] Range[0, nmax]!
Table[Sum[Abs[StirlingS1[n, k]] HypergeometricU[-k/2, 1/2, -1/2]/(-1/2)^(k/2), {k, 0, n}], {n, 0, 22}]
PROG
(PARI) my(x='x + O('x^25)); Vec(serlaplace(exp(log(1 - x)^2/2)/(1 - x))) \\ Michel Marcus, Jan 24 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jan 21 2019
STATUS
approved