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 A377823 #17 Nov 21 2024 09:04:11
%S A377823 0,1,4,10,23,50,110,240,526,1147,2489,5368,11510,24543,52090,110109,
%T A377823 231959,487245,1020980,2134838,4455582,9283742,19314740,40128699,
%U A377823 83265342,172564435,357228078,738707908,1526004117,3149310585,6493394292,13376521031,27532616663
%N A377823 Sum of the positions of maximum parts in all compositions of n.
%F A377823 G.f.: A(x) = d/dy A(x,y)|_{y = 1}, where A(x,y) = Sum_{i>0} (x^i * y^(i*(i+1)/2)) + Sum_{m>1} (Sum_{i>0} (x^m * y^i * ((x-x^m)/(1-x))^(i-1) * (Sum_{j>=0} (Product_{u=1..j} ((x-x^m)/(1-x) + x^m * y^(u+i)) ) ) ) ).
%e A377823 The composition of 7, (1,2,1,1,2) has maximum parts at positions 2 and 5; so it contributes 7 to a(7) = 240.
%o A377823 (PARI)
%o A377823 A_xy(N) = {my(x='x+O('x^N), h = sum(i=1,N, y^(i*(i+1)/2)*x^i)+sum(m=2,N, sum(i=1,N, ((y^i)*x^m)*((x-x^m)/(1-x))^(i-1)*(sum(j=0,N-m-i, prod(u=1,j, (x-x^m)/(1-x)+(y^(u+i))*x^m)))))); h}
%o A377823 P_xy(N) = Pol(A_xy(N), {x})
%o A377823 A_x(N) = {my(px = deriv(P_xy(N),y), y=1); Vecrev(eval(px))}
%o A377823 A_x(20)
%Y A377823 Cf. A001792, A010054, A011782, A097976, A097979, A377824.
%K A377823 nonn,easy
%O A377823 0,3
%A A377823 _John Tyler Rascoe_, Nov 08 2024