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

1,1

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.

Links

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

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

Example

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

Prog

(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

Crossrefs

Row sums give A235792.

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

Sequence in context: A260361 A055935 A086930 * A099585 A236959 A366032

Adjacent sequences: A235795 A235796 A235797 * A235799 A235800 A235801

Keyword

nonn,tabl

Author

Omar E. Pol, Jan 18 2014

Extensions

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

Status

approved