OFFSET
0,2
COMMENTS
Equals triple binomial transform of A014182.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..500
FORMULA
E.g.f.: exp(2*x+1-exp(-x)) = 1+3*x+8*x^2/2!+19*x^3/3!+....
a(n) = exp(1)*Sum_{k >= 0} (-1)^k*(2-k)^n/k!. Cf. A126617. - Peter Bala, Oct 28 2011.
G.f.: (G(0) - 1)/(x-1) where G(k) = 1 - 1/(1+k*x-2*x)/(1-x/(x-1/G(k+1) )); (recursively defined continued fraction). - Sergei N. Gladkovskii, Jan 17 2013
a(0) = 1; a(n) = 2*a(n-1) - Sum_{k=1..n} (-1)^k * binomial(n-1,k-1) * a(n-k). - Ilya Gutkovskiy, Dec 01 2023
EXAMPLE
a(3) = 19 = (1, 3, 3, 1) dot (1, 2, 3, 3) = (1 + 6 + 9 + 3); where A109747 = (1, 2, 3, 3, 2, 3, 5, -4, 5, 55, -212, ...).
MATHEMATICA
Join[{1}, Rest[CoefficientList[Series[Exp[2*x + 1 - Exp[-x]], {x, 0, 50}], x]*Range[0, 50]!]] (* G. C. Greubel, Aug 31 2016 *)
CROSSREFS
KEYWORD
sign
AUTHOR
Gary W. Adamson, Dec 31 2008
STATUS
approved