A281231 Exponential transform of the tetrahedral numbers (A000292).

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

Table of n, a(n) for n=0..21.

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

Index to sequences related to pyramidal numbers

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

Cf. A000292, A279361, A279358.

Sequence in context: A078509 A239820 A077240 * A356010 A244786 A129098

Adjacent sequences: A281228 A281229 A281230 * A281232 A281233 A281234

Keyword

nonn

Author

Ilya Gutkovskiy, Jan 18 2017

Status

approved