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A360653
Irregular table read by rows; the first row contains the value 1, and for n > 1, the n-th row lists the numbers of the form binomial(m-1, k) such that binomial(m, k) = n.
3
1, 1, 1, 2, 1, 3, 1, 4, 1, 3, 5, 1, 6, 1, 7, 1, 8, 1, 4, 6, 9, 1, 10, 1, 11, 1, 12, 1, 13, 1, 5, 10, 14, 1, 15, 1, 16, 1, 17, 1, 18, 1, 10, 19, 1, 6, 15, 20, 1, 21, 1, 22, 1, 23, 1, 24, 1, 25, 1, 26, 1, 7, 21, 27, 1, 28, 1, 29, 1, 30, 1, 31, 1, 32, 1, 33, 1, 15, 20, 34
OFFSET
1,4
COMMENTS
In other words, the n-th rows lists the numbers that appear directly above n in Pascal's triangle (A007318).
The n-th row starts with 1, ends with n-1 (provided that n > 1), and contains other values iff n belongs to A006987.
EXAMPLE
Table begins:
n n-th row
-- -------------
1 1
2 1
3 1, 2
4 1, 3
5 1, 4
6 1, 3, 5
7 1, 6
8 1, 7
9 1, 8
10 1, 4, 6, 9
11 1, 10
.
For n = 6:
Pascal's triangle begins as follows:
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
1 6 15 20 15 6 1
we find the value 6 in row 4 below 3 and 3, and in row 6 below 1 and 5,
so the 6th row contains 1, 3 and 5.
PROG
(PARI) See Links section.
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Rémy Sigrist, Feb 15 2023
STATUS
approved