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)).

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

Seiichi Manyama, Antidiagonals n = 0..139, flattened

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.

Cf. A306646, A306680.

Sequence in context: A166556 A275257 A325027 * A275937 A321317 A338092

Adjacent sequences: A306732 A306733 A306734 * A306736 A306737 A306738

Keyword

nonn,tabl

Author

Seiichi Manyama, Mar 06 2019

Status

approved