cp's OEIS Frontend

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.

A235798 Triangle read by rows: T(n,k) = number of occurrences of k in all overpartitions of n.

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%I A235798 #19 Feb 19 2020 21:47:01
%S A235798 2,4,2,10,4,2,20,8,4,2,38,16,8,4,2,68,30,16,8,4,2,118,52,28,16,8,4,2,
%T A235798 196,88,48,28,16,8,4,2,318,144,82,48,28,16,8,4,2,504,230,132,80,48,28,
%U A235798 16,8,4,2,782,360,208,128,80,48,28,16,8,4,2,1192,552,324,202,128,80,48,28,16,8,4,2
%N A235798 Triangle read by rows: T(n,k) = number of occurrences of k in all overpartitions of n.
%C A235798 It appears that row n lists the first differences of row n of triangle A235797 together with 2 (as the final term of the row).
%C A235798 The equivalent sequence for partitions is A066633.
%H A235798 Andrew Howroyd, <a href="/A235798/b235798.txt">Table of n, a(n) for n = 1..1275</a> (first 50 rows)
%F A235798 G.f. of column k: 2*(x^k/((1 - x^k)*(1 + x^k))) * Product_{j>0} (1 + x^j)/(1 - x^j). - _Andrew Howroyd_, Feb 19 2020
%e A235798 Triangle begins:
%e A235798 2;
%e A235798 4,   2;
%e A235798 10,  4,  2;
%e A235798 20,  8,  4,  2;
%e A235798 38, 16,  8,  4,  2;
%e A235798 68, 30, 16,  8,  4,  2;
%e A235798 ...
%o A235798 (PARI)
%o A235798 A(n)={my(p=prod(k=1, n, (1 + x^k)/(1 - x^k) + O(x*x^n))); Mat(vector(n, k, Col(2*(p + O(x*x^(n-k)))*x^k/((1 - x^k)*(1 + x^k)), -n)))}
%o A235798 { my(T=A(10)); for(n=1, #T, print(T[n, 1..n])) } \\ _Andrew Howroyd_, Feb 19 2020
%Y A235798 Row sums give A235792.
%Y A235798 Cf. A015128, A066633, A235790, A235793, A235797, A236000, A236001.
%K A235798 nonn,tabl
%O A235798 1,1
%A A235798 _Omar E. Pol_, Jan 18 2014
%E A235798 Terms a(22) and beyond from _Andrew Howroyd_, Feb 19 2020