login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A193931 E.g.f. A(x) = exp(x+x^2+x^3+x^4+x^5). 3
1, 1, 3, 13, 73, 501, 3331, 27553, 253233, 2540233, 27340291, 309811701, 3843476473, 50560182973, 701098196163, 10205952248521, 155809733115361, 2506135027165713, 42013633806350083, 732584456250306013, 13270900741926553641, 249625454707702681861 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..500

FORMULA

a(n)=n!*sum(k=1..n, sum(i=0..(n-k)/5, (-1)^i*binomial(k,k-i)*binomial(n-5*i-1,k-1))/k!), n>0, a(0)=1.

E.g.f.: 1 + x*(E(0)-1)/(x+1) where E(k) =  1 + (1+x+x^2+x^3+x^4)/(k+1)/(1-x/(x+1/E(k+1) )); (recursively defined continued fraction). - Sergei N. Gladkovskii, Jan 27 2013

MAPLE

a:= proc(n) option remember; `if`(n=0, 1, add(

      a(n-j)*binomial(n-1, j-1)*j!, j=1..min(n, 5)))

    end:

seq(a(n), n=0..23);  # Alois P. Heinz, Sep 29 2017

PROG

(Maxima)

a(n):=if n=0 then 1 else n!*sum(sum((-1)^i*binomial(k, k-i)*binomial(n-5*i-1, k-1), i, 0, (n-k)/5)/k!, k, 1, n);

CROSSREFS

Sequence in context: A205776 A132846 A293196 * A293197 A193932 A193933

Adjacent sequences:  A193928 A193929 A193930 * A193932 A193933 A193934

KEYWORD

nonn

AUTHOR

Vladimir Kruchinin, Aug 09 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
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 26 02:14 EDT 2021. Contains 348256 sequences. (Running on oeis4.)