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A306735
Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of g.f. ((k+1-x)*(1-x)^(k-1))/((1-x)^k-x^(k+1)).
3
1, 2, 1, 3, 1, 1, 4, 2, 3, 1, 5, 3, 2, 4, 1, 6, 4, 3, 5, 7, 1, 7, 5, 4, 3, 10, 11, 1, 8, 6, 5, 4, 7, 17, 18, 1, 9, 7, 6, 5, 4, 18, 29, 29, 1, 10, 8, 7, 6, 5, 9, 39, 51, 47, 1, 11, 9, 8, 7, 6, 5, 28, 73, 90, 76, 1, 12, 10, 9, 8, 7, 6, 11, 74, 127, 158, 123, 1, 13, 11, 10, 9, 8, 7, 6, 40, 164, 219, 277, 199, 1
OFFSET
0,2
LINKS
FORMULA
A(n,k) = A306646(k*n,k) for k > 0.
A(n,k) = (k+1)*A306680(n,k) - A306680(n-1,k) for n > 0.
EXAMPLE
Square array begins:
1, 2, 3, 4, 5, 6, 7, 8, 9, ...
1, 1, 2, 3, 4, 5, 6, 7, 8, ...
1, 3, 2, 3, 4, 5, 6, 7, 8, ...
1, 4, 5, 3, 4, 5, 6, 7, 8, ...
1, 7, 10, 7, 4, 5, 6, 7, 8, ...
1, 11, 17, 18, 9, 5, 6, 7, 8, ...
1, 18, 29, 39, 28, 11, 6, 7, 8, ...
1, 29, 51, 73, 74, 40, 13, 7, 8, ...
1, 47, 90, 127, 164, 125, 54, 15, 8, ...
CROSSREFS
Columns 0-2 give A000012, A000032, A259967.
Sequence in context: A166556 A275257 A325027 * A275937 A321317 A338092
KEYWORD
nonn,tabl
AUTHOR
Seiichi Manyama, Mar 06 2019
STATUS
approved