A104533 == A129682

[Maximilian Hasler]

http://www.research.att.com/~njas/sequences/?q=A104533%7Cid%3AA129682
obviously the same -
the definition of A129682 is to be the expansion of the e.g.f. of A104533 !
Initial term a(0)=1 can be added to A104533
and comment / 2nd formula from A129682.
A129682 can be deleted or remain as placeholder / "redirect" to A104533.

Neil, you told you dislike receiving complete "EDITS" of big records,
so I just put what should change:

%S A104533 0,2,12,104,1168,16032,259264,4817024,100954368,2353435136,60355677184,
1687701792768,51077784506368,1662782678736896,57917727119818752,
2148722382829027328,84569896954751942656,3518839711497761980416
%C A129682 a(n)=2^n*A000262(n). - Paul Barry (pbarry(AT)wit.ie), Apr 28 2007
%F A129682 E.g.f.: exp(2x/(1-2x)); a(n)=2^n*n!*sum{k=0..n,
C(n-1,k)/(k+1)!}. - Paul Barry (pbarry(AT)wit.ie), Apr 28 2007
%O A104533 0,2

Maximilian

On Sat, May 3, 2008 at 5:11 AM, Joerg Arndt <arndt at jjj.de> wrote:
> ... mod initial term, merge?
>  (at least crossref!)



In pari/gp:

\\ A061256   Euler transform of sigma(n), cf. A000203. 
1/prod(j=1,N,eta(x^j)^j);
Vec(%)

\\ A006171   Number of factorization patterns of polynomials of degree n over integers.
1/prod(j=1,N,eta(x^j));
Vec(%)

\\ A107742   G.f.: Product(Product(1+x^(i*j),i=1..infinity),j=1..infinity).
1/prod(j=0,N,eta(x^(2*j+1)));
Vec(%)
1/prod(j=0,N,eta(-x^(2*j+1))); \\ A107742 with different signs
Vec(%)

\\ A004101 Number of partitions of n of the form a_1*b_1^2 + a_2*b_2^2 + ... 
1/prod(j=1,N,eta(x^(j^2)));
Vec(%)

\\ start (up to 191) matches A024792   Number of 8's in all partitions of n. 
1/prod(j=1,N3,eta(x^(j^3)));
Vec(%)

Any comments, verifications, complaints etc. welcome.



Again pari/gp:

N=17
default(seriesprecision,N);
x=z+O(z^(N+1))

c=sum(j=1,N,j*x^j); \\ log case
\\ z + 3/2*z^2 + 4/3*z^3 + 7/4*z^4 + 6/5*z^5 + 2*z^6 + 8/7*z^7 + 15/8*z^8 + ...
\\ z + 3*z^2 + 4*z^3 + 7*z^4 + 6*z^5 + 12*z^6 + 8*z^7 + 15*z^8 + ...
v=Vec(s)
\\ [1, 3, 4, 7, 6, 12, 8, 15, 13, 18, 12, 28, 14, 24, 24, 31, 18]
\\ this is A000203 as advertised


Replace the line s=-log(...) with one of the following to
obtain other seqs from the OEIS:
\\ etc. you get he picture



Should these guys go as comments/formulas to the respective seqs?