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

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A183241 G.f.: A(x) = exp( Sum_{n>=1} A183240(n)*x^n/n ) where A183240 is the sums of the squares of multinomial coefficients. 5
1, 1, 3, 18, 213, 4128, 122638, 5096305, 284192429, 20375905738, 1829560187405, 200829815300994, 26471873341135571, 4124649654997542447, 750006492020987263020, 157382918361825037892997 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Conjectured to consist entirely of integers.

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..250

FORMULA

a(n) = (1/n)*Sum_{k=1..n} A183240(k)*a(n-k) for n>0 with a(0)=1.

a(n) ~ c * n! * (n-1)!, where c = Product_{k>=2} 1/(1-1/(k!)^2) = 1.37391178018464563291... . - Vaclav Kotesovec, Feb 19 2015

EXAMPLE

G.f.: A(x) = 1 + x + 3*x^2 + 18*x^3 + 213*x^4 + 4128*x^5 +...

log(A(x)) = x + 5*x^2/2 + 46*x^3/3 + 773*x^4/4 + 19426*x^5/5 + 708062*x^6/6 + 34740805*x^7/7 +...+ A183240(n)*x^n/n +...

PROG

(PARI) {a(n)=polcoeff(exp(intformal(1/x*(-1+serlaplace(serlaplace(1/prod(k=1, n+1, 1-x^k/k!^2+O(x^(n+2)))))))), n)}

CROSSREFS

Cf. A183240, A183239.

Sequence in context: A157538 A024488 A217902 * A163883 A319580 A132727

Adjacent sequences:  A183238 A183239 A183240 * A183242 A183243 A183244

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jan 04 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 December 13 03:41 EST 2019. Contains 329968 sequences. (Running on oeis4.)