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

Author

Ilya Gutkovskiy, Jan 18 2017

Keywords

• nonn

Examples

			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! + ...
		

Links

• 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

Crossrefs

Cf. A000292, A279361, A279358.

Programs

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]

Formula

E.g.f.: exp(exp(x)*x*(1+x+x^2/6)).