This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A224678 #9 May 05 2025 20:26:59
%S A224678 1,1,4,5,6,16,22,29,49,86,122,188,300,456,714,1117,1718,2653,4124,
%T A224678 6390,9916,15368,23806,36884,57181,88622,137344,212896,329934,511316,
%U A224678 792516,1228285,1903598,2950334,4572602,7086833,10983562,17022956,26382984,40889694,63373086,98218920
%N A224678 L.g.f.: -log(1 - Sum_{n>=1} x^(n*(n+1)/2)) = Sum_{n>=1} a(n)*x^n/n.
%F A224678 Logarithmic derivative of A023361, where A023361(n) = number of compositions of n into positive triangular numbers.
%e A224678 L.g.f.: L(x) = x + x^2/2 + 4*x^3/3 + 5*x^4/4 + 6*x^5/5 + 16*x^6/6 + 22*x^7/7 + 29*x^8/8 + 49*x^9/9 + 86*x^10/10 +...
%e A224678 where
%e A224678 exp(L(x)) = 1 + x + x^2 + 2*x^3 + 3*x^4 + 4*x^5 + 7*x^6 + 11*x^7 + 16*x^8 + 25*x^9 + 40*x^10 + 61*x^11 + 94*x^12 +...+ A023361(n)*x^n +...
%e A224678 exp(-L(x)) = 1 - x - x^3 - x^6 - x^10 - x^21 - x^28 +...+ -x^(n*(n+1)/2) +...
%o A224678 (PARI) {a(n)=n*polcoeff(-log(1-sum(r=1, sqrtint(2*n+1), x^(r*(r+1)/2)+x*O(x^n))), n)}
%o A224678 for(n=1, 50, print1(a(n), ", "))
%Y A224678 Cf. A023361, A219331, A224680.
%K A224678 nonn
%O A224678 1,3
%A A224678 _Paul D. Hanna_, Apr 14 2013