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A174740 Triangle read by rows, A027293 * an infinite lower triangular matrix with A147843 as the diagonal and the rest zeros. 2
1, 1, 2, 2, 2, 0, 3, 4, 0, 0, 5, 6, 0, 0, -5, 7, 10, 0, 0, -5, 0, 11, 14, 0, 0, -10, 0, -7, 15, 22, 0, 0, -15, 0, -7, 0, 22, 30, 0, 0, -25, 0, -14, 0, 0, 30, 44, 0, 0, -35, 0, -21, 0, 0, 0, 42, 60, 0, 0, -55, 0, -35, 0, 0, 0, 0, 56, 84, 0, 0, -75, 0, -49, 0, 0, 0, 0, 12 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
Left border = the partition numbers, A000041; right border = A147843 starting (1, 2, 0, ...).
Row sums apparently give A000203. Check: Sum of row 6 terms = [7, 5, 3, 2, 1, 1] dot [1, 2, 0, 0, -5, 0] = [7 + 10 + 0 + 0 -5 + 0] = 12 = A000203(6).
LINKS
FORMULA
Equals triangle A027293 * a lower triangular matrix with A147843 (deleting the first zero) as the right border and the rest zeros.
T(n,k) = A147843(k) * A027293(n,k). - Joerg Arndt, Dec 29 2022
EXAMPLE
First few rows of the triangle:
1;
1, 2;
2, 2, 0;
3, 4, 0, 0;
5, 6, 0, 0, -5;
7, 10, 0, 0, -5, 0;
11, 14, 0, 0, -10, 0, -7;
15, 22, 0, 0, -15, 0, -7, 0;
22, 30, 0, 0, -25, 0, -14, 0, 0;
30, 44, 0, 0, -35, 0, -21, 0, 0, 0;
42, 60, 0, 0, -55, 0, -35, 0, 0, 0, 0;
56, 84, 6, 0, -75, 0, -49, 0, 0, 0, 0, 12;
...
CROSSREFS
Sequence in context: A071441 A134577 A071442 * A124759 A071295 A296062
KEYWORD
tabl,sign
AUTHOR
Gary W. Adamson, Mar 28 2010
EXTENSIONS
Terms corrected by Gary W. Adamson, Dec 27 2022
STATUS
approved

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Last modified July 24 02:09 EDT 2024. Contains 374575 sequences. (Running on oeis4.)