A327482 Irregular triangle read by rows where T(n,d) is the number of integer partitions of n with mean d|n.

1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 3, 3, 1, 1, 1, 1, 5, 4, 1, 1, 7, 1, 1, 7, 5, 1, 1, 1, 1, 11, 15, 12, 6, 1, 1, 1, 1, 15, 7, 1, 1, 30, 19, 1, 1, 22, 34, 8, 1, 1, 1, 1, 30, 58, 27, 9, 1, 1, 1, 1, 42, 84, 64, 10, 1, 1, 105, 37, 1, 1, 56, 11, 1

Offset

1,7

Links

Table of n, a(n) for n=1..74.

Example

Triangle begins:
  1
  1  1
  1  1
  1  2  1
  1  1
  1  3  3  1
  1  1
  1  5  4  1
  1  7  1
  1  7  5  1
  1  1
  1 11 15 12  6  1
  1  1
  1 15  7  1
  1 30 19  1
  1 22 34  8  1

Mathematica

Table[Length[Select[IntegerPartitions[n], Mean[#]==d&]], {n, 20}, {d, Divisors[n]}]

Crossrefs

Row sums are A067538.

The version for subsets is A327481.

Cf. A066571, A237984, A240850, A327474, A327483, A327484.

Sequence in context: A181386 A193517 A296554 * A189006 A245013 A219924

Adjacent sequences: A327479 A327480 A327481 * A327483 A327484 A327485

Keyword

nonn,tabf

Author

Gus Wiseman, Sep 13 2019

Status

approved