A098546 Table read by rows: row n has a term T(n,k) for each of the partition(n) partitions of n. T(n,k) = binomial(n,m) where m is the number of parts.
1, 2, 1, 3, 3, 1, 4, 6, 6, 4, 1, 5, 10, 10, 10, 10, 5, 1, 6, 15, 15, 15, 20, 20, 20, 15, 15, 6, 1, 7, 21, 21, 21, 35, 35, 35, 35, 35, 35, 35, 21, 21, 7, 1, 8, 28, 28, 28, 28, 56, 56, 56, 56, 56, 70, 70, 70, 70, 70, 56, 56, 56, 28, 28, 8, 1, 9, 36, 36, 36, 36, 84, 84, 84, 84, 84, 84, 84
Offset: 1
Examples
A036042 begins 1 2 2 3 3 3 4 4 4 4 4 ... A036043 begins 1 1 2 1 2 3 1 2 2 3 4 ... so a(n) begins 1 2 1 3 3 1 4 6 6 4 1 ... Table begins . 1 2 1 3 3 1 4 6 6 4 1 5 10 10 10 10 5 1 6 15 15 20 15 20 15 20 15 6 1 .
Links
- M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
Programs
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Mathematica
Table[Sequence @@ Map[Function[p, Binomial[n, Length[p]]], IntegerPartitions[n]], {n, 1, 10}] (* Olivier Gérard, May 07 2024 *)
Comments