|
%I #8 Sep 04 2017 04:12:51
%S 1,3,19,223,4771,190023,14441659,2130394591,616038609331,
%T 351153716973303,395928966997611499,885010943452285951183,
%U 3928049212346654960720611,34658088824057172975437120103,608435145369338712372672919898779,21266998855813018955669706360248449471
%N L.g.f.: A(x) = log( Sum_{n>=0} 2^[n(n-1)/2]*x^n ).
%H Vincenzo Librandi, <a href="/A136652/b136652.txt">Table of n, a(n) for n = 1..80</a>
%e L.g.f.: A(x) = x + 3*x^2/2 + 19*x^3/3 + 223*x^4/4 + 4771*x^5/5 +...
%e A(x) = log(1 + x + 2x^2 + 8x^3 + 64x^4 + 1024x^5 +...+ 2^(n(n-1)/2)*x^n +...).
%t max = 14; s = Log[Sum[2^(k*(k-1)/2)*x^k, {k, 0, max}]] + O[x]^(max+1); CoefficientList[s, x]*Range[0, max] // Rest (* _Jean-François Alcover_, Sep 03 2017 *)
%o (PARI) a(n)=n*polcoeff(log(sum(k=0,n,2^(k*(k-1)/2)*x^k +x*O(x^n))),n)
%Y Cf. A136653, A136654.
%K nonn
%O 1,2
%A _Paul D. Hanna_, Jan 15 2008
|
