OFFSET
0,2
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..150
FORMULA
Binomial transform of A051295.
G.f.: (1 + x/((1-x)*S(0) - x))/(1-x), where S(k) = 1 - (k+1)*x/(1 - x - (k+1)*x/S(k+1)); (continued fraction). - Sergei N. Gladkovskii, Feb 05 2015
a(n) ~ exp(1) * (n-1)!. - Vaclav Kotesovec, Feb 06 2015
EXAMPLE
a(3) = 15 = (1, 3, 3, 1) dot (1, 1, 2, 5) = 1 + 3 + 6 + 5, where A051295 = (1, 1, 2, 5, 15, 54, 235, ...).
MATHEMATICA
max = 20; Clear[g]; g[max + 2] = 1; g[k_] := g[k] = 1 - (k+1)*x/(1 - x - (k+1)*x/g[k+1]; gf = (1 + x/((1-x)*g[0] -x))/(1-x); CoefficientList[Series[gf, {x, 0, max}], x] (* Vaclav Kotesovec, Feb 06 2015, after Sergei N. Gladkovskii *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Gary W. Adamson, Oct 22 2007
EXTENSIONS
More terms from Vaclav Kotesovec, Feb 06 2015
STATUS
approved