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A330377
Irregular triangle read by rows: T(n,k) is the sum of all parts of all partitions of n with Durfee square of size k, (n >= 1; 1 <= k <= floor(sqrt(n))).
0
1, 4, 9, 16, 4, 25, 10, 36, 30, 49, 56, 64, 112, 81, 180, 9, 100, 300, 20, 121, 440, 55, 144, 660, 120, 169, 910, 234, 196, 1274, 420, 225, 1680, 735, 256, 2240, 1184, 16, 289, 2856, 1870, 34, 324, 3672, 2844, 90, 361, 4560, 4199, 190, 400, 5700, 6040, 400, 441, 6930, 8547, 714, 484, 8470, 11792, 1298
OFFSET
1,2
FORMULA
T(n,k) = n*A115994(n,k).
EXAMPLE
Triangle begins:
1;
4;
9;
16, 4;
25, 10;
36, 30;
49, 56;
64, 112;
81, 180, 9;
100, 300, 20;
121, 440, 55;
144, 660, 120;
169, 910, 234;
196, 1274, 420;
225, 1680, 735;
256, 2240, 1184, 16;
289, 2856, 1870, 34;
324, 3672, 2844, 90;
361, 4560, 4199, 190;
400, 5700, 6040, 400;
441, 6930, 8547, 714;
484, 8470, 11792, 1298;
...
CROSSREFS
Row sums give A066186.
Row lengths give A000196, n >= 1.
Column 1 gives A000290, n >= 1.
Column k starts at row k^2 with k^2.
Cf. A115994.
Sequence in context: A120866 A070443 A279403 * A070643 A070442 A086957
KEYWORD
nonn,tabf
AUTHOR
Omar E. Pol, Dec 22 2019
STATUS
approved