cp's OEIS Frontend

A266693 Number of partitions of n with product of multiplicities of parts equal to 10.

%I A266693 #11 May 24 2018 09:51:26
%S A266693 0,0,0,0,0,0,0,0,0,1,1,1,3,4,2,7,8,12,13,19,22,32,36,46,64,72,88,112,
%T A266693 134,160,203,236,287,343,412,477,577,676,798,944,1101,1283,1516,1754,
%U A266693 2030,2361,2738,3157,3657,4202,4826,5567,6356,7279,8340,9494,10815
%N A266693 Number of partitions of n with product of multiplicities of parts equal to 10.
%H A266693 Alois P. Heinz, <a href="/A266693/b266693.txt">Table of n, a(n) for n = 0..10000</a>
%F A266693 a(n) ~ c * exp(Pi*sqrt(n/3)) * n^(1/4), where c = 0.007782666499... - _Vaclav Kotesovec_, May 24 2018
%e A266693 a(9) = 1: [1,1,1,1,1,2,2].
%e A266693 a(12) = 3: [1,1,1,1,1,1,1,1,1,1,2], [1,1,2,2,2,2,2], [1,1,1,1,1,2,2,3].
%e A266693 a(13) = 4: [1,1,1,1,1,1,1,1,1,1,3], [1,1,1,1,1,2,3,3], [1,1,1,1,1,2,2,4], [1,1,1,1,1,4,4].
%p A266693 b:= proc(n, i, p) option remember; `if`(i*(p+(i-1)/2)<n, 0, `if`(n=0,
%p A266693       `if`(p=1, 1, 0), b(n, i-1, p) +add(`if`(irem(p, j)>0, 0, (h->
%p A266693        b(h, min(h, i-1), p/j))(n-i*j)), j=1..min(p, n/i))))
%p A266693     end:
%p A266693 a:= b(n$2, 10):
%p A266693 seq(a(n), n=0..65);
%t A266693 b[n_, i_, p_] := b[n, i, p] = If[i*(p + (i - 1)/2) < n, 0, If[n == 0, If[p == 1, 1, 0], b[n, i - 1, p] + Sum[If[Mod[p, j] > 0, 0, Function[h, b[h, Min[h, i - 1], p/j]][n - i*j]], {j, 1, Min[p, n/i]}]]];
%t A266693 a[n_] := b[n, n, 10];
%t A266693 Table[a[n], {n, 0, 65}] (* _Jean-François Alcover_, May 01 2018, translated from Maple *)
%Y A266693 Column k=10 of A266477.
%K A266693 nonn
%O A266693 0,13
%A A266693 _Emeric Deutsch_ and _Alois P. Heinz_, Jan 02 2016