OFFSET
0,5
FORMULA
a(n) = sum(k=0..(n-1)/2, binomial(2*k,k)*2^(-2*k)*(-1)^(k)*(2*k+1)!*stirling1(n,2*k+1)), n>0.
MATHEMATICA
Table[Sum[Binomial[2 k, k] 2^(-2 k) (-1)^k * (2 k + 1)! * StirlingS1[n, 2 k + 1], {k, 0, (n - 1)/2}], {n, 0, 23}] (* Michael De Vlieger, Jul 13 2015 *)
PROG
(Maxima)
a(n):=sum(binomial(2*k, k)*2^(-2*k)*(-1)^(k)*(2*k+1)!*stirling1(n, 2*k+1), k, 0, (n-1)/2);
(PARI) x='x+O('x^33); concat([0], Vec(serlaplace(sin(atan(log(1+x)))))) \\ Joerg Arndt, Jul 13 2015
CROSSREFS
KEYWORD
sign
AUTHOR
Vladimir Kruchinin, Jun 17 2011
EXTENSIONS
Terms corrected by Anders Claesson, Jul 13 2015
STATUS
approved