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

0,2

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).

Example

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}.

Crossrefs

Cf. A209406, A360626.

Sequence in context: A184263 A058408 A053906 * A316539 A197964 A100236

Adjacent sequences: A359959 A359960 A359961 * A359963 A359964 A359965

Keyword

nonn

Author

Alois P. Heinz, Jan 20 2023

Status

approved