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A266687 Number of partitions of n with product of multiplicities of parts equal to 4. 2
0, 0, 0, 0, 1, 0, 2, 1, 3, 4, 6, 6, 11, 13, 17, 24, 29, 36, 48, 59, 72, 96, 111, 138, 170, 207, 245, 305, 362, 432, 517, 616, 723, 868, 1013, 1194, 1412, 1644, 1915, 2245, 2605, 3019, 3511, 4051, 4677, 5410, 6209, 7125, 8199, 9372, 10718, 12257, 13975, 15902 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,7

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..18694 (terms 0..10000 from Alois P. Heinz)

FORMULA

a(n) ~ c * exp(Pi*sqrt(n/3)) * n^(1/4), where c = 0.0108735520090052... - Vaclav Kotesovec, May 24 2018

EXAMPLE

a(6) = 2: [1,1,1,1,2], [1,1,2,2].

a(7) = 1: [1,1,1,1,3].

a(8) = 3: [2,2,2,2], [1,1,3,3], [1,1,1,1,4].

a(9) = 4: [1,2,2,2,2], [1,1,1,1,2,3], [1,1,2,2,3], [1,1,1,1,5].

a(10) = 6: [1,1,2,3,3], [2,2,3,3], [1,1,1,1,2,4], [1,1,2,2,4], [1,1,4,4], [1,1,1,1,6].

MAPLE

b:= proc(n, i, p) option remember; `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..n/i)))

    end:

a:= n-> b(n$2, 4):

seq(a(n), n=0..70);

MATHEMATICA

b[n_, i_, p_] := b[n, i, p] = 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, n/i}]]]; a[n_] := b[n, n, 4]; Table[a[n], {n, 0, 70}] (* Jean-Fran├žois Alcover, Dec 22 2016, after Alois P. Heinz *)

CROSSREFS

Column k=4 of A266477.

Sequence in context: A098164 A158504 A293253 * A060214 A259773 A030133

Adjacent sequences:  A266684 A266685 A266686 * A266688 A266689 A266690

KEYWORD

nonn

AUTHOR

Emeric Deutsch and Alois P. Heinz, Jan 02 2016

STATUS

approved

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Last modified August 19 04:07 EDT 2018. Contains 313843 sequences. (Running on oeis4.)