A279361 Exponential transform of the triangular numbers.

1, 1, 4, 16, 80, 471, 3127, 23059, 186468, 1635265, 15422471, 155388399, 1663294756, 18826525771, 224434810797, 2808247979611, 36770685485408, 502505495269521, 7150461569849395, 105723461155720879, 1621191824611307436, 25738508587975433251

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..519

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, Triangular Number

Index to sequences related to polygonal numbers

Formula

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

Example

E.g.f.: A(x) = 1 + x/1! + 4*x^2/2! + 16*x^3/3! + 80*x^4/4! + 471*x^5/5! + 3127*x^6/6! + ...

Maple

a:= proc(n) option remember; `if`(n=0, 1,
      add(binomial(n-1, j-1)*j*(j+1)/2*a(n-j), j=1..n))
    end:
seq(a(n), n=0..25);  # Alois P. Heinz, Dec 11 2016

Mathematica

Range[0, 23]! CoefficientList[Series[Exp[Exp[x] x (x + 2)/2], {x, 0, 23}], x]

Crossrefs

Cf. A000217, A033462.

Sequence in context: A171454 A316944 A020080 * A003471 A002777 A280923

Adjacent sequences: A279358 A279359 A279360 * A279362 A279363 A279364

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 10 2016

Status

approved