|
|
|
|
|
|
|
|
|
#14 by Joerg Arndt at Sun Aug 18 13:00:53 EDT 2013
|
|
|
|
|
|
|
|
#13 by Vaclav Kotesovec at Sun Aug 18 12:53:03 EDT 2013
|
|
|
|
|
|
|
|
#12 by Vaclav Kotesovec at Sun Aug 18 12:52:19 EDT 2013
|
|
| LINKS
|
Vaclav Kotesovec, <a href="/A199876/a199876.txt">TITLE FOR LINKRecurrence</a>
|
|
| FORMULA
|
a(n) ~ c*d^n/n^(3/2), where d=7.9486365297943819... is the root of the equation -729 + 4374*d - 10827*d^2 + 13770*d^3 + 13095*d^4 + 28404*d^5 - 4664*d^6 + 108*d^7 = 0 and c = 0.2415824543... (note that the term with root d=35.7258 tends to zero). - Vaclav Kotesovec, Aug 18 2013
|
|
| MATHEMATICA
|
nmax=20; aa=ConstantArray[0, nmax]; aa[[1]]=1; Do[AGF=1+Sum[aa[[n]]*x^n, {n, 1, j-1}]+koef*x^j; sol=Solve[Coefficient[(1+x*AGF^3)*(1+x^2*AGF^3)-AGF, x, j]==0, koef][[1]]; aa[[j]]=koef/.sol[[1]], {j, 2, nmax}]; Flatten[{1, aa}] (* Vaclav Kotesovec, Aug 18 2013 *)
|
|
|
|
|
|
|
#11 by Vaclav Kotesovec at Sun Aug 18 12:50:51 EDT 2013
|
|
| LINKS
|
Vaclav Kotesovec, <a href="/A199876/a199876.txt">TITLE FOR LINK</a>
|
|
|
|
|
|
|
#10 by Vaclav Kotesovec at Sun Aug 18 12:50:19 EDT 2013
|
|
| LINKS
|
Vaclav Kotesovec, <a href="/A199876/b199876.txt">Table of n, a(n) for n = 0..300</a>
|
|
| STATUS
|
approved
editing
|
|
|
|
|
|
|
#9 by Russ Cox at Fri Mar 30 18:37:32 EDT 2012
|
|
| AUTHOR
|
_Paul D. Hanna (pauldhanna(AT)juno.com), _, Nov 11 2011
|
|
|
|
|
Discussion
|
| Fri Mar 30
| 18:37
| OEIS Server: https://oeis.org/edit/global/213
|
|
|
|
|
|
|
#8 by T. D. Noe at Fri Nov 11 13:17:49 EST 2011
|
|
|
|
|
|
|
|
#7 by Paul D. Hanna at Fri Nov 11 12:02:13 EST 2011
|
|
|
|
|
|
|
|
#6 by Paul D. Hanna at Fri Nov 11 12:02:11 EST 2011
|
|
| FORMULA
|
G.f. A(x) satisfies:
G.f. satisfies: (1) A(x) = exp( Sum_{n>=1} [Sum_{k=0..n} C(n,k)^2 * x^k] * x^n*A(x)^(2*n)/n ).
(2) A(x) = exp( Sum_{n>=1} [(1-x)^(2*n+1)*Sum_{k>=0} C(n+k,k)^2*x^k )] * x^n*A(x)^(2*n)/n.
|
|
| STATUS
|
proposed
editing
|
|
|
|
|
|
|
#5 by Paul D. Hanna at Fri Nov 11 11:54:42 EST 2011
|
|
|
|
|
|
|
