OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..519
M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to arXiv version]
M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to Lin. Alg. Applic. version together with omitted figures]
N. J. A. Sloane, Transforms
Eric Weisstein's World of Mathematics, Exponential Transform
Eric Weisstein's World of Mathematics, Triangular Number
FORMULA
E.g.f.: exp(exp(x)*x*(x+2)/2).
EXAMPLE
E.g.f.: A(x) = 1 + x/1! + 4*x^2/2! + 16*x^3/3! + 80*x^4/4! + 471*x^5/5! + 3127*x^6/6! + ...
MAPLE
a:= proc(n) option remember; `if`(n=0, 1,
add(binomial(n-1, j-1)*j*(j+1)/2*a(n-j), j=1..n))
end:
seq(a(n), n=0..25); # Alois P. Heinz, Dec 11 2016
MATHEMATICA
Range[0, 23]! CoefficientList[Series[Exp[Exp[x] x (x + 2)/2], {x, 0, 23}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Dec 10 2016
STATUS
approved