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A359962 Number of multisets of n nonempty words with a total of 2n letters over binary alphabet. 3

%I #26 Feb 14 2023 12:31:06

%S 1,4,26,132,623,2632,10500,39384,141659,490100,1644186,5366436,

%T 17113433,53454528,163963312,494786352,1471423866,4318092136,

%U 12520027756,35901819336,101909674398,286575107424,798886300056,2209115439664,6062818714752,16522049256656

%N Number of multisets of n nonempty words with a total of 2n letters over binary alphabet.

%H Alois P. Heinz, <a href="/A359962/b359962.txt">Table of n, a(n) for n = 0..500</a>

%F a(n) = [x^(2*n)*y^n] Product_{j>=1} 1/(1-y*x^j)^(2^j).

%F a(n) = A209406(2n,n).

%e a(0) = 1: {}.

%e a(1) = 4: {aa}, {ab}, {ba}, {bb}.

%e 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}.

%Y Cf. A209406, A360626.

%K nonn

%O 0,2

%A _Alois P. Heinz_, Jan 20 2023

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