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 A293741 Number of sets of nonempty words with a total of n letters over binary alphabet such that within each prefix of a word every letter of the alphabet is at least as frequent as the subsequent alphabet letter. 5
 1, 1, 2, 5, 10, 23, 51, 111, 243, 530, 1156, 2497, 5421, 11662, 25179, 53991, 116035, 248025, 531045, 1131943, 2415495, 5135914, 10927905, 23182313, 49199819, 104154950, 220543471, 465997148, 984704560, 2076988713, 4380764650, 9225209928, 19424814305 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..1000 FORMULA G.f.: Product_{j>=1} (1+x^j)^A001405(j). MAPLE b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0, add(       b(n-i*j, i-1)*binomial(binomial(i, floor(i/2)), j), j=0..n/i)))     end: a:= n-> b(n\$2): seq(a(n), n=0..35); MATHEMATICA b[n_, i_] := b[n, i] = If[n == 0, 1, If[i < 1, 0, Sum[b[n - i*j, i - 1]* Binomial[Binomial[i, Floor[i/2]], j], {j, 0, n/i}]]]; a[n_] := b[n, n]; Table[a[n], {n, 0, 35}] (* Jean-François Alcover, May 29 2019, after Alois P. Heinz *) PROG (Python) from sympy.core.cache import cacheit from sympy import binomial, floor @cacheit def b(n, i): return 1 if n==0 else 0 if i<1 else sum([b(n - i*j, i - 1)*binomial(binomial(i, floor(i//2)), j) for j in range(n//i + 1)]) def a(n): return b(n, n) print(map(a, range(36))) # Indranil Ghosh, Oct 15 2017 CROSSREFS Column k=2 of A293112. Cf. A001405. Sequence in context: A087640 A116953 A099516 * A291559 A297074 A099963 Adjacent sequences:  A293738 A293739 A293740 * A293742 A293743 A293744 KEYWORD nonn AUTHOR Alois P. Heinz, Oct 15 2017 STATUS approved

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Last modified May 8 05:46 EDT 2021. Contains 343653 sequences. (Running on oeis4.)