OFFSET
0,3
COMMENTS
Logarithmic transform of A036968.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..430
N. J. A. Sloane, Transforms
Wikipedia, Genocchi number
EXAMPLE
E.g.f.: A(x) = x - 2*x^2/2! + 5*x^3/3! - 20*x^4/4! + 109*x^5/5! - 738*x^6/6! + ...
MAPLE
a:= proc(n) option remember; (t-> `if`(n=0, 0, t(n)-add(a(j)*j*
t(n-j)*binomial(n, j), j=1..n-1)/n))(i-> i*euler(i-1, 0))
end:
seq(a(n), n=0..25); # Alois P. Heinz, Dec 04 2018
MATHEMATICA
nmax = 22; CoefficientList[Series[Log[1 + 2 x/(Exp[x] + 1)], {x, 0, nmax}], x] Range[0, nmax]!
a[n_] := a[n] = n EulerE[n - 1, 0] - Sum[k Binomial[n, k] (n - k) EulerE[n - k - 1, 0] a[k], {k, 1, n - 1}]/n; a[0] = 0; Table[a[n], {n, 0, 22}]
a[n_] := a[n] = 2 (1 - 2^n) BernoulliB[n] - Sum[k Binomial[n, k] 2 (1 - 2^(n - k)) BernoulliB[n - k] a[k], {k, 1, n - 1}]/n; a[0] = 0; Table[a[n], {n, 0, 22}]
CROSSREFS
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Jun 14 2018
STATUS
approved