cp's OEIS Frontend

A206139 G.f.: A(x) = Sum_{n>=0} x^(n*(n+1)/2) / Product_{k=1..n} (1-x^k)^(n-k+1).

%I A206139 #7 Aug 21 2018 09:53:29
%S A206139 1,1,1,2,3,5,8,13,21,34,55,88,141,224,356,563,890,1401,2202,3448,5386,
%T A206139 8386,13025,20175,31180,48077,73976,113588,174057,266174,406224,
%U A206139 618729,940552,1427038,2161122,3266956,4930052,7427314,11171332,16776169,25154204
%N A206139 G.f.: A(x) = Sum_{n>=0} x^(n*(n+1)/2) / Product_{k=1..n} (1-x^k)^(n-k+1).
%H A206139 Vaclav Kotesovec, <a href="/A206139/b206139.txt">Table of n, a(n) for n = 0..400</a>
%e A206139 G.f.: A(x) = 1 + x + x^2 + 2*x^3 + 3*x^4 + 5*x^5 + 8*x^6 + 13*x^7 +...
%e A206139 where
%e A206139 A(x) = 1 + x/(1-x) + x^3/((1-x)^2*(1-x^2)) + x^6/((1-x)^3*(1-x^2)^2*(1-x^3)) + x^10/((1-x)^4*(1-x^2)^3*(1-x^3)^2*(1-x^4)) +...
%o A206139 (PARI) {a(n)=polcoeff(sum(m=0,n,x^(m*(m+1)/2)/prod(k=1,m,(1-x^k +x*O(x^n))^(m-k+1))),n)}
%o A206139 for(n=0,61,print1(a(n),", "))
%Y A206139 Cf. A206119.
%K A206139 nonn
%O A206139 0,4
%A A206139 _Paul D. Hanna_, Feb 04 2012