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

0,3

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

Formula

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

Example

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! + ...

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]

Crossrefs

Cf. A000578, A033462.

Column k=3 of A279636.

Sequence in context: A282179 A278000 A159598 * A344820 A156544 A094793

Adjacent sequences: A279355 A279356 A279357 * A279359 A279360 A279361

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 10 2016

Status

approved