A281231 - OEIS

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

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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))

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