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A279358 Exponential transform of the cubes A000578. 6
1, 1, 9, 52, 413, 3916, 41077, 481384, 6198425, 86430160, 1296040841, 20763245944, 353272341061, 6353672109760, 120315348389069, 2390488408994536, 49682962883210033, 1077292416660660736, 24313317132393295633, 569937590287796925784, 13850459183086300341341 (list; graph; refs; listen; history; text; internal format)
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 * A156544 A094793 A197499

Adjacent sequences:  A279355 A279356 A279357 * A279359 A279360 A279361

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Dec 10 2016

STATUS

approved

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Last modified August 10 19:52 EDT 2020. Contains 336381 sequences. (Running on oeis4.)