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G.f.: A(x) = Sum_{n>=0} x^(n*(n+1)/2) / Product_{k=1..n} (1-x^k)^(n-k+1).
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%I #7 Aug 21 2018 09:53:29

%S 1,1,1,2,3,5,8,13,21,34,55,88,141,224,356,563,890,1401,2202,3448,5386,

%T 8386,13025,20175,31180,48077,73976,113588,174057,266174,406224,

%U 618729,940552,1427038,2161122,3266956,4930052,7427314,11171332,16776169,25154204

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

%H Vaclav Kotesovec, <a href="/A206139/b206139.txt">Table of n, a(n) for n = 0..400</a>

%e G.f.: A(x) = 1 + x + x^2 + 2*x^3 + 3*x^4 + 5*x^5 + 8*x^6 + 13*x^7 +...

%e where

%e 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 (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 for(n=0,61,print1(a(n),", "))

%Y Cf. A206119.

%K nonn

%O 0,4

%A _Paul D. Hanna_, Feb 04 2012