A320346 -id:A320346

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A360335

Array read by antidiagonals downwards: A(n,m) = number of set partitions of [2n] into 2-element subsets {i, i+k} with 1 <= k <= m.

+0
5

1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 3, 7, 5, 1, 1, 3, 12, 16, 8, 1, 1, 3, 15, 35, 38, 13, 1, 1, 3, 15, 63, 105, 89, 21, 1, 1, 3, 15, 90, 226, 329, 209, 34, 1, 1, 3, 15, 105, 417, 841, 1014, 491, 55, 1, 1, 3, 15, 105, 645, 1787, 3251, 3116, 1153, 89, 1

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

1,5

LINKS

Table of n, a(n) for n=1..66.

FORMULA

A(n,m) = A001147(n) = A104443(n,2) for m >= 2n - 1.

EXAMPLE

Square array begins:

1, 1, 1, 1, 1, 1, 1, 1, 1, ...

1, 2, 3, 3, 3, 3, 3, 3, 3, ...

1, 3, 7, 12, 15, 15, 15, 15, 15, ...

1, 5, 16, 35, 63, 90, 105, 105, 105, ...

1, 8, 38, 105, 226, 417, 645, 840, 945, ...

1, 13, 89, 329, 841, 1787, 3348, 5445, 7665, ...

1, 21, 209, 1014, 3251, 7938, 16717, 31647, 53250, ...

1, 34, 491, 3116, 12483, 36500, 86311, 180560, 344403, ...

1, 55, 1153, 9610, 47481, 167631, 459803, 1062435, 2211181, ...

...

CROSSREFS

Main diagonal is A014307.

Columns 1..4 are A000012, A000045(n+1), A052967, A320346.

Cf. A001147, A104443, A360333, A360334.

KEYWORD

nonn,tabl

AUTHOR

Peter Dolland, Feb 03 2023

STATUS

approved

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