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!)
A126342 Denominators of the limit of coefficients of q in { [x^n] W(x,q) } when read backward from [q^(n*(n-1)/2)] to [q^(n*(n-1)/2 - (n-1))], where W satisfies: W(x,q) = exp( q*x*W(q*x,q) ). 3
1, 2, 1, 6, 1, 1, 24, 3, 12, 3, 40, 2, 8, 8, 4, 720, 120, 240, 360, 120, 120, 840, 360, 72, 720, 120, 360, 720, 40320, 1680, 10080, 630, 4032, 5040, 672, 560, 72576, 840, 40320, 120960, 1920, 40320, 24192, 8064, 2520, 3628800, 362880, 145152, 4536, 725760 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

When the fractions {A126341(k)/A126342(k), k>=1} are formatted as a triangle in which row n is then multiplied by n!, the result is integer triangle A126343.

LINKS

Table of n, a(n) for n=0..49.

FORMULA

A126341(n)/A126342(n) = A126265(n, n*(n-1)/2) / n! for n>=1.

EXAMPLE

The function W that satisfies: W(x,q) = exp( q*x*W(q*x,q) ) begins:

W(x,q) = 1 + q*x + (1/2 + q)*q^2*x^2 +

(1/6 + 1*q + 1/2*q^2 + 1*q^3)*q^3*x^3 +

(1/24 + 1/2*q + 1*q^2 + 7/6*q^3 + 1*q^4 + 1/2*q^5 + 1*q^6)*q^4*x^4 +...

Coefficients of q in {[x^n] W(x,q)} tend to a limit when read backwards:

n=1: [1, 1/2];

n=2: [1, 1/2, 1, 1/6];

n=3: [1, 1/2, 1, 7/6, 1, 1/2, 1/24].

The limit of coefficients of q in { [x^n] W(x,q) } begins:

[1, 1/2, 1, 7/6, 2, 2, 85/24, 11/3, 65/12, 19/3, 357/40, 19/2, 111/8, 123/8, 81/4, 16891/720,...].

PROG

(PARI) {a(n)=local(W=1+x); for(i=0, n, W=exp(subst(x*W, x, q*x+O(x^(n+2))))); denominator(Vec(Vec(W)[n+2]+O(q^(n*(n+1)/2+2)))[n*(n-1)/2+1])}

CROSSREFS

Cf. A126341 (numerators), A126343, A126265.

Sequence in context: A290318 A139547 A323855 * A229818 A324500 A082388

Adjacent sequences:  A126339 A126340 A126341 * A126343 A126344 A126345

KEYWORD

frac,nonn

AUTHOR

Paul D. Hanna, Dec 25 2006

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 7 20:33 EST 2019. Contains 329849 sequences. (Running on oeis4.)