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A266499 Number of partitions of n with product of multiplicities of parts equal to n. 2
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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

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Last modified April 10 15:07 EDT 2021. Contains 342845 sequences. (Running on oeis4.)