OFFSET
0,3
COMMENTS
Empirically, for odd n, n|a(n) and for even n, (n-1)|a(n).
LINKS
Robert Israel, Table of n, a(n) for n = 0..418
FORMULA
a(n) = 1-2n*a(n-1)-Sum_{k=0..n-2}binomial(n,k)*2^(n-k-1)*a(k)
a(n) = Sum_{k=0..n} Sum_{j=0..k} Sum_{i=0..n} binomial(n,k)*binomial(k+i,i)*binomial(n,i)(i!*(-1)^(i+j)*(2j+1)^(n-i))/(2^k)
a(n) ~ n! * (-1)^n*sqrt(LambertW(exp(-1)))*2^(n+1) / (1+LambertW(exp(-1)))^(n+2). - Vaclav Kotesovec, May 03 2016
MAPLE
S:= series(2*exp(x)/(exp(2*x)+1+2*x), x, 31):
seq(coeff(S, x, j)*j!, j=0..30); # Robert Israel, May 24 2016
MATHEMATICA
a[n_]:=Sum[Sum[Sum[Binomial[k, j]*Binomial[k + i, i]*Binomial[n, i]*((i!*(-1)^(i + j)*(2 j + 1)^(n - i))/(2^k)), {i, 0, n}], {j, 0, k}], {k, 0, n}]
CROSSREFS
KEYWORD
sign
AUTHOR
Christopher Ernst, Apr 22 2016
STATUS
approved