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 A254686 Number of ways to put n red and n blue balls into n indistinguishable boxes. 4
 1, 1, 5, 19, 74, 248, 814, 2457, 7168, 19928, 53688, 139820, 354987, 878434, 2128102, 5052010, 11781881, 27019758, 61035671, 135928105, 298784144, 648726349, 1392474574, 2956730910, 6214668074, 12937060340, 26686392239, 54572423946, 110680119454, 222710856175, 444776676764 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS See a comment on A254811 about multiset partitions and the Knuth reference. - Wolfdieter Lang, Mar 26 2015 LINKS Brian Chen, Table of n, a(n) for n = 0..64 EXAMPLE 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). MAPLE with(numtheory): b:= proc(n, k, i) option remember; `if`(n>k, 0, 1) +`if`(isprime(n) or i<2, 0, add( `if`(d>k, 0, b(n/d, d, i-1)), d=divisors(n) minus {1, n})) end: a:= n-> b(6^n\$2, n): seq(a(n), n=0..20); # Alois P. Heinz, Mar 26 2015 MATHEMATICA 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 *) CROSSREFS Cf. A002774, A060150, A254811. Column k=2 of A256384. Main diagonal of A277239. Sequence in context: A149765 A124464 A149766 * A295374 A212403 A098913 Adjacent sequences: A254683 A254684 A254685 * A254687 A254688 A254689 KEYWORD nonn AUTHOR Brian Chen, Feb 08 2015 STATUS approved

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Last modified December 4 03:42 EST 2023. Contains 367541 sequences. (Running on oeis4.)