OFFSET
0,4
COMMENTS
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..65
FORMULA
G.f.: x/(1-x)^2 = Sum_{n>=0} a(n)*x^n/(1-3^n*x).
By using the inverse transformation: a(n) = Sum_{k=0..n} k*A118183(n-k)*(3^k)^(n-k) for n>=0.
a(3^n) is divisible by 3^n.
EXAMPLE
Column 0 of log(A118180) = [0, 1, -1/2, 3/3, -23/4, 329/5, 18231/6, ...].
The g.f. is illustrated by:
x/(1-x)^2 = x + 2*x^2 + 3*x^3 + 4*x^4 + 5*x^5 + 6*x^6 + ...
= x/(1-3*x) - x^2/(1-9*x) + 3*x^3/(1-27*x) - 23*x^4/(1-81*x) + 329*x^5/(1-243*x) + 18231*x^6/(1-729*x) - 22030373*x^7/(1-2187*x) + ...
MATHEMATICA
a[n_]:= a[n]= -Sum[3^(j*(n-j))*j*A118183[j], {j, 0, n}];
Table[a[n], {n, 0, 30}] (* G. C. Greubel, Jun 29 2021 *)
PROG
(PARI) {a(n)=local(T=matrix(n+1, n+1, r, c, if(r>=c, (3^(c-1))^(r-c))), L=sum(m=1, #T, -(T^0-T)^m/m)); return(n*L[n+1, 1])}
(Sage)
@CachedFunction
def a(n): return (-1)*sum( 3^(j*(n-j))*j*A118183(j) for j in (0..n))
[a(n) for n in (0..30)] # G. C. Greubel, Jun 29 2021
CROSSREFS
KEYWORD
sign
AUTHOR
Paul D. Hanna, Apr 15 2006
STATUS
approved