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

Author

Emeric Deutsch and Alois P. Heinz, Dec 30 2015

Keywords

• nonn

Examples

			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.
		

Links

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

Crossrefs

Main diagonal of A266477.

Cf. A000040, A000041.

Programs

Maple

b:= proc(n, i, p) option remember; `if`(p=1 and i*(i+1)/2 `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 *)

Formula

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

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