A235798 - OEIS

%I #19 Feb 19 2020 21:47:01

%S 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 196,88,48,28,16,8,4,2,318,144,82,48,28,16,8,4,2,504,230,132,80,48,28,

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

%C 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 The equivalent sequence for partitions is A066633.

%H Andrew Howroyd, <a href="/A235798/b235798.txt">Table of n, a(n) for n = 1..1275</a> (first 50 rows)

%F 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 Triangle begins:

%e 2;

%e 4,   2;

%e 10,  4,  2;

%e 20,  8,  4,  2;

%e 38, 16,  8,  4,  2;

%e 68, 30, 16,  8,  4,  2;

%e ...

%o (PARI)

%o 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 { my(T=A(10)); for(n=1, #T, print(T[n, 1..n])) } \\ _Andrew Howroyd_, Feb 19 2020

%Y Row sums give A235792.

%Y Cf. A015128, A066633, A235790, A235793, A235797, A236000, A236001.

%K nonn,tabl

%O 1,1

%A _Omar E. Pol_, Jan 18 2014

%E Terms a(22) and beyond from _Andrew Howroyd_, Feb 19 2020