login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A203227 (n-1)-st elementary symmetric function of (0!,...,(n-1)!) 4
1, 2, 5, 32, 780, 93888, 67633920, 340899840000, 13745206960128000, 4987865758275993600000, 18099969098565397826764800000, 722492853172221856076141690880000000, 346075232923849611911833538569175040000000000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Each term appears as an unreduced numerator in the following partial infinite sum: f(0) = 1; f(n) = f(n-1)/n; Sum_{k>=0}(f(k)) = e. - Daniel Suteu, Jul 30 2016

a(n)/A000178(n-1) -> e as n -> oo. - Daniel Suteu, Jul 30 2016

LINKS

Table of n, a(n) for n=1..13.

EXAMPLE

For n=4, the 3rd elementary symmetric polynomial in the 4 variables a, b, c, and d is abc + abd + acd + bcd. Setting a = 0! = 1, b = 1! = 1, c = 2! = 2, and d = 3! = 6 gives a(4) = 1*1*2 + 1*1*6 + 1*2*6 + 1*2*6 = 2 + 6 + 12 + 12 = 32. - Michael B. Porter, Aug 17 2016

MATHEMATICA

f[k_] := (k - 1)!; t[n_] := Table[f[k], {k, 1, n}]

a[n_] := SymmetricPolynomial[n - 1, t[n]]

Table[a[n], {n, 1, 14}]

Flatten[{1, Table[Det[Table[BellB[i+j], {i, n}, {j, n}]], {n, 1, 15}]}] (* Vaclav Kotesovec, Nov 28 2016 *)

CROSSREFS

Cf. A203228, A000142, A000178.

Sequence in context: A019036 A005636 A067299 * A207135 A118325 A224231

Adjacent sequences:  A203224 A203225 A203226 * A203228 A203229 A203230

KEYWORD

nonn

AUTHOR

Clark Kimberling, Dec 30 2011

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 21 08:27 EDT 2018. Contains 316405 sequences. (Running on oeis4.)