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URL: https://oeis.org/A235798

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A235798
Triangle read by rows: T(n,k) = number of occurrences of k in all overpartitions of n.
9
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
KEYWORD
nonn,tabl
AUTHOR
Omar E. Pol, Jan 18 2014
EXTENSIONS
Terms a(22) and beyond from Andrew Howroyd, Feb 19 2020
STATUS
approved