A266499 Number of partitions of n with product of multiplicities of parts equal to n.

0, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 2, 1, 2, 2, 8, 1, 5, 1, 11, 6, 5, 1, 48, 7, 9, 21, 39, 1, 104, 1, 143, 27, 20, 45, 457, 1, 32, 58, 620, 1, 549, 1, 363, 514, 65, 1, 4302, 118, 858, 207, 926, 1, 4080, 437, 5171, 382, 181, 1, 20398, 1, 251, 4287, 20582, 1212

Offset

0,9

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Formula

a(n) = A266477(n,n).

p in primes => a(p) = 1.

Example

a(8) = 2 because among the 22 (= A000041(8)) partitions of 8 only [1,1,1,1,1,1,1,1] and [1,1,1,1,2,2] have product of multiplicities of parts equal to 8.

Maple

b:= proc(n, i, p) option remember; `if`(p=1 and i*(i+1)/2<n, 0,
     `if`(n=0, `if`(p=1, 1, 0), `if`(i<1, 0, b(n, i-1, p)+add(
     `if`(irem(p, j)=0, b(n-i*j, i-1, p/j), 0), j=1..min(p, n/i)))))
    end:
a:= n-> `if`(isprime(n), 1, b(n$3)):
seq(a(n), n=0..70);

Mathematica

b[n_, i_, p_] := b[n, i, p] = If[p == 1 && i*(i + 1)/2 < n, 0, If[n == 0, If[p == 1, 1, 0], If[i < 1, 0, b[n, i - 1, p] + Sum[If[Mod[p, j] == 0, b[n - i*j, i - 1, p/j], 0], {j, 1, Min[p, n/i]}]]]]; a[n_] := If[PrimeQ[n], 1, b[n, n, n]]; Table[a[n], {n, 0, 70}] (* Jean-François Alcover, Dec 22 2016, after Alois P. Heinz *)

Crossrefs

Main diagonal of A266477.

Cf. A000040, A000041.

Sequence in context: A124767 A319443 A130633 * A226621 A112933 A270650

Adjacent sequences: A266496 A266497 A266498 * A266500 A266501 A266502

Keyword

nonn

Author

Emeric Deutsch and Alois P. Heinz, Dec 30 2015

Status

approved