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A281231
Exponential transform of the tetrahedral numbers (A000292).
2
1, 1, 5, 23, 133, 916, 7107, 61286, 580505, 5968400, 66032901, 780962524, 9817927385, 130572957724, 1829676460991, 26919714974436, 414591408939313, 6665930432840304, 111624874150941193, 1942675652654112012, 35071252458352443001, 655641049733709757516
OFFSET
0,3
LINKS
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, Tetrahedral Number
FORMULA
E.g.f.: exp(exp(x)*x*(1+x+x^2/6)).
EXAMPLE
E.g.f.: A(x) = 1 + x/1! + 5*x^2/2! + 23*x^3/3! + 133*x^4/4! + 916*x^5/5! + 7107*x^6/6! + ...
MAPLE
a:= proc(n) option remember; `if`(n=0, 1, add(a(n-j)
*binomial(n-1, j-1)*j*(j+1)*(j+2)/6, j=1..n))
end:
seq(a(n), n=0..25); # Alois P. Heinz, Jan 18 2017
MATHEMATICA
Range[0, 21]! CoefficientList[Series[Exp[Exp[x] x (1 + x + x^2/6)], {x, 0, 21}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jan 18 2017
STATUS
approved