A279358 Exponential transform of the cubes A000578.

1, 1, 9, 52, 413, 3916, 41077, 481384, 6198425, 86430160, 1296040841, 20763245944, 353272341061, 6353672109760, 120315348389069, 2390488408994536, 49682962883210033, 1077292416660660736, 24313317132393295633, 569937590287796925784, 13850459183086300341341

Offset: 0

Author

Ilya Gutkovskiy, Dec 10 2016

Keywords

• nonn

Examples

			E.g.f.: A(x) = 1 + x/1! + 9*x^2/2! + 52*x^3/3! + 413*x^4/4! + 3916*x^5/5! + 41077*x^6/6! + ...
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..479
• 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, Cubic Number

Crossrefs

Cf. A000578, A033462.

Column k=3 of A279636.

Programs

Maple

a:= proc(n) option remember; `if`(n=0, 1,
      add(binomial(n-1, j-1)*j^3*a(n-j), j=1..n))
    end:
seq(a(n), n=0..25);  # Alois P. Heinz, Dec 11 2016

Mathematica

Range[0, 20]! CoefficientList[Series[Exp[Exp[x] (x + 3 x^2 + x^3)], {x, 0, 20}], x]

Formula

E.g.f.: exp(exp(x)*(x+3*x^2+x^3)).