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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 (list; graph; refs; listen; history; text; internal format)
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 * A244786 A129098 A047049

Adjacent sequences:  A281228 A281229 A281230 * A281232 A281233 A281234

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Jan 18 2017

STATUS

approved

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Last modified December 3 14:51 EST 2020. Contains 338906 sequences. (Running on oeis4.)