A373029 - OEIS

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A373029

Triangle T(n,k), n >= 0, 0 <= k <= n, read by rows, where T(n,k) is the number of distinct partitions p of n such that max(p) is a multiple of k.

2

1, 0, 1, 0, 1, 1, 0, 2, 1, 1, 0, 2, 1, 1, 1, 0, 3, 1, 1, 1, 1, 0, 4, 2, 2, 1, 1, 1, 0, 5, 3, 1, 2, 1, 1, 1, 0, 6, 3, 1, 2, 2, 1, 1, 1, 0, 8, 4, 3, 2, 2, 2, 1, 1, 1, 0, 10, 5, 3, 2, 3, 2, 2, 1, 1, 1, 0, 12, 6, 4, 2, 3, 3, 2, 2, 1, 1, 1, 0, 15, 7, 6, 3, 3, 4, 3, 2, 2, 1, 1, 1, 0, 18, 9, 6, 4, 3, 4, 4, 3, 2, 2, 1, 1, 1

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OFFSET

0,8

LINKS

Table of n, a(n) for n=0..104.

FORMULA

For k > 0, g.f. of column k: Sum_{i>=0} x^(k*i) * Product_{j=1..k*i-1} (1+x^j).

EXAMPLE

Triangle begins:

1;

0, 1;

0, 1, 1;

0, 2, 1, 1;

0, 2, 1, 1, 1;

0, 3, 1, 1, 1, 1;

0, 4, 2, 2, 1, 1, 1;

0, 5, 3, 1, 2, 1, 1, 1;

0, 6, 3, 1, 2, 2, 1, 1, 1;

0, 8, 4, 3, 2, 2, 2, 1, 1, 1;

0, 10, 5, 3, 2, 3, 2, 2, 1, 1, 1;

0, 12, 6, 4, 2, 3, 3, 2, 2, 1, 1, 1;

0, 15, 7, 6, 3, 3, 4, 3, 2, 2, 1, 1, 1;

0, 18, 9, 6, 4, 3, 4, 4, 3, 2, 2, 1, 1, 1;

CROSSREFS

Row sums give A373030.

Column k=0..3 give A000007, A000009, A026838, A372893.

T(2n,n) gives A000009.

Sequence in context: A083661 A029369 A255315 * A125072 A162642 A366246

Adjacent sequences: A373026 A373027 A373028 * A373030 A373031 A373032

KEYWORD

nonn,tabl

AUTHOR

Seiichi Manyama, May 20 2024

STATUS

approved