A279787 Twice-partitioned numbers where the first partition is constant.

1, 1, 3, 4, 10, 8, 29, 16, 64, 58, 124, 57, 469, 102, 489, 763, 1597, 298, 3858, 491, 8942, 6355, 6187, 1256, 59076, 18766, 20830, 49694, 167078, 4566, 481186, 6843, 752128, 362907, 231592, 1597802, 5951007, 21638, 790404, 2655810, 25274798, 44584, 40898731

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..5723

Gus Wiseman, Illustration of the first 9 terms of A279787

Gus Wiseman, Sequences enumerating triangles of integer partitions

Formula

a(n) = Sum_{d|n} A000041(n/d)^d for n > 0. - Andrew Howroyd, Aug 26 2018

Example

The a(4)=10 twice-partitions are:
((4)), ((31)), ((22)), ((211)), ((1111)),
((2)(2)), ((2)(11)), ((11)(2)), ((11)(11)),
((1)(1)(1)(1)).

Maple

with(numtheory): with(combinat):
a:= proc(n) option remember; `if`(n=0, 1,
      add(numbpart(n/d)^d, d=divisors(n)))
    end:
seq(a(n), n=0..70);  # Alois P. Heinz, Dec 20 2016

Mathematica

nn=20; Table[DivisorSum[n, Power[PartitionsP[#], n/#]&], {n, nn}]

Prog

(PARI) a(n)=if(n==0, 1, sumdiv(n, d, numbpart(n/d)^d)) \\ Andrew Howroyd, Aug 26 2018

Crossrefs

Cf. A000005, A000041, A018818, A063834, A260685, A271619.

Sequence in context: A356150 A222136 A339652 * A128488 A359366 A226303

Adjacent sequences: A279784 A279785 A279786 * A279788 A279789 A279790

Keyword

nonn

Author

Gus Wiseman, Dec 18 2016

Status

approved