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A254686 Number of ways to put n red and n blue balls into n indistinguishable boxes.

%I A254686 #26 Oct 06 2016 18:23:44
%S A254686 1,1,5,19,74,248,814,2457,7168,19928,53688,139820,354987,878434,
%T A254686 2128102,5052010,11781881,27019758,61035671,135928105,298784144,
%U A254686 648726349,1392474574,2956730910,6214668074,12937060340,26686392239,54572423946,110680119454,222710856175,444776676764
%N A254686 Number of ways to put n red and n blue balls into n indistinguishable boxes.
%C A254686 See a comment on A254811 about multiset partitions and the Knuth reference. - _Wolfdieter Lang_, Mar 26 2015
%H A254686 Brian Chen, <a href="/A254686/b254686.txt">Table of n, a(n) for n = 0..64</a>
%e A254686 For n = 2 the a(2) = 5 ways to put 2 red balls and 2 blue balls into 2 indistinguishable boxes are (RRBB)(), (RRB)(B), (RBB)(R), (RR)(BB), (RB)(RB).
%p A254686 with(numtheory):
%p A254686 b:= proc(n, k, i) option remember;
%p A254686       `if`(n>k, 0, 1) +`if`(isprime(n) or i<2, 0, add(
%p A254686       `if`(d>k, 0, b(n/d, d, i-1)), d=divisors(n) minus {1, n}))
%p A254686     end:
%p A254686 a:= n-> b(6^n$2,n):
%p A254686 seq(a(n), n=0..20);  # _Alois P. Heinz_, Mar 26 2015
%t A254686 b[n_, k_, i_] := b[n, k, i] = If[n > k, 0, 1] + If[PrimeQ[n] || i < 2, 0, Sum[If[d > k, 0, b[n/d, d, i - 1]], {d, Divisors[n] [[2 ;; -2]]}]]; a[n_] := b[6^n, 6^n, n]; Table[a[n], {n, 0, 20}] (* _Jean-François Alcover_, Jan 08 2016, after _Alois P. Heinz_ *)
%Y A254686 Cf. A002774, A060150, A254811.
%Y A254686 Column k=2 of A256384.
%Y A254686 Main diagonal of A277239.
%K A254686 nonn
%O A254686 0,3
%A A254686 _Brian Chen_, Feb 08 2015