OFFSET
0,3
LINKS
Robert Israel, Table of n, a(n) for n = 0..453
FORMULA
a(n) = Sum_{k=0..n} |Stirling1(n,k)|*A067994(k).
MAPLE
E:= 1/(1-x)^log(1-x):
S:= series(E, x, 31):
seq(coeff(S, x, j)*j!, j=0..30); # Robert Israel, May 22 2019
MATHEMATICA
nmax = 23; CoefficientList[Series[1/(1 - x)^Log[1 - x], {x, 0, nmax}], x] Range[0, nmax]!
Table[Sum[Abs[StirlingS1[n, k]] HermiteH[k, 0], {k, 0, n}], {n, 0, 23}]
a[n_] := a[n] = -2 Sum[(k - 1)! HarmonicNumber[k - 1] Binomial[n - 1, k - 1] a[n - k], {k, 2, n}]; a[0] = 1; Table[a[n], {n, 0, 23}]
PROG
(PARI) a(n) = sum(k=0, n, abs(stirling(n, k, 1))*polhermite(k, 0)); \\ Michel Marcus, May 21 2019
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( (1-x)^Log(1/(1-x)) )); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, May 21 2019
(Sage) m = 30; T = taylor((1-x)^log(1/(1-x)), x, 0, m); [factorial(n)*T.coefficient(x, n) for n in (0..m)] # G. C. Greubel, May 21 2019
CROSSREFS
KEYWORD
sign,look
AUTHOR
Ilya Gutkovskiy, May 21 2019
STATUS
approved