cp's OEIS Frontend

Examples

			For n = 5 and k = 3 the diagram of regions of the set of partitions of 5 contains three parts that start in the third column: two parts of size 1 and one part of size 2, therefore the sum of all parts that start in column 3 is 1 + 1 + 2 = 4, so T(5,3) = 4.
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.                       Illustration of the parts
.    Diagram             that start in column k:
.    for n=5       k=1          k=2  k=3    k=4    k=5
.   _ _ _ _ _       _ _ _ _ _
.  |_ _ _    |     |_ _ _ _ _|               _ _
.  |_ _ _|_  |     |_ _ _|_                 |_ _|   _
.  |_ _    | |     |_ _ _ _|          _ _          |_|
.  |_ _|_  | |     |_ _|_            |_ _|   _     |_|
.  |_ _  | | |     |_ _ _|            _     |_|    |_|
.  |_  | | | |     |_ _|         _   |_|    |_|    |_|
.  |_|_|_|_|_|     |_|          |_|  |_|    |_|    |_|
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k = 1 2 3 4 5
.
The 5th row lists:  20           1    4      5      5
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Triangle begins:
1;
3,   1;
6,   1,  2;
12,  1,  4,  3;
20,  1,  4,  5,  5;
35,  1,  6,  8,  9,  7;
54,  1,  6, 10, 12, 11, 11;
86,  1,  8, 13, 20, 14, 19, 15;
128, 1,  8, 18, 23, 22, 25, 23, 22;
192, 1, 10, 21, 34, 30, 37, 29, 36, 30;
275, 1, 10, 26, 41, 41, 48, 41, 45, 46, 42;
399, 1, 12, 32, 56, 53, 72, 52, 67, 58, 66, 56;