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

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

Offset: 1

Author

Omar E. Pol, Jan 18 2014

Keywords

• nonn
• tabl

Comments

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).

The equivalent sequence for partitions is A066633.

Examples

			Triangle begins:
2;
4,   2;
10,  4,  2;
20,  8,  4,  2;
38, 16,  8,  4,  2;
68, 30, 16,  8,  4,  2;
...
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..1275 (first 50 rows)

Crossrefs

Row sums give A235792.

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

Programs

PARI

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)))}
{ my(T=A(10)); for(n=1, #T, print(T[n, 1..n])) } \\ Andrew Howroyd, Feb 19 2020

Formula

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

Extensions

Terms a(22) and beyond from Andrew Howroyd, Feb 19 2020