A359962 Number of multisets of n nonempty words with a total of 2n letters over binary alphabet.
1, 4, 26, 132, 623, 2632, 10500, 39384, 141659, 490100, 1644186, 5366436, 17113433, 53454528, 163963312, 494786352, 1471423866, 4318092136, 12520027756, 35901819336, 101909674398, 286575107424, 798886300056, 2209115439664, 6062818714752, 16522049256656
Offset: 0
Keywords
Examples
a(0) = 1: {}.
a(1) = 4: {aa}, {ab}, {ba}, {bb}.
a(2) = 26: {a,aaa}, {a,aab}, {a,aba}, {a,abb}, {a,baa}, {a,bab}, {a,bba}, {a,bbb}, {aa,aa}, {aa,ab}, {aa,ba}, {aa,bb}, {aaa,b}, {aab,b}, {ab,ab}, {ab,ba}, {ab,bb}, {aba,b}, {abb,b}, {b,baa}, {b,bab}, {b,bba}, {b,bbb}, {ba,ba}, {ba,bb}, {bb,bb}.
Links
- Alois P. Heinz, Table of n, a(n) for n = 0..500
Formula
a(n) = [x^(2*n)*y^n] Product_{j>=1} 1/(1-y*x^j)^(2^j).
a(n) = A209406(2n,n).