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A261043
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Number of multisets of nonempty words with a total of n letters over binary alphabet such that all letters occur at least once in the multiset.
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3
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0, 0, 3, 14, 49, 148, 427, 1170, 3150, 8288, 21562, 55368, 140998, 355854, 892014, 2220856, 5497483, 13533264, 33150801, 80825768, 196218139, 474423934, 1142756063, 2742781794, 6561049181, 15645058210, 37194447065, 88174246904, 208463588035, 491585765888
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) ~ c^2 * 2^(n-1) * exp(2*sqrt(n) - 1/2) / (sqrt(Pi) * n^(3/4)), where c = A247003 = exp( Sum_{k>=2} 1/(k*(2^k-2)) ) = 1.3976490050836502...
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MATHEMATICA
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CoefficientList[Series[Product[1/(1-x^k)^(2^k), {k, 1, 30}] - 2*Product[1/(1 - x^k), {k, 1, 30}] + 1, {x, 0, 30}], x]
(* Second program: *)
A[n_, k_] := A[n, k] = If[n == 0, 1, Sum[DivisorSum[j, #*k^# &]*A[n - j, k], {j, 1, n}]/n];
T[n_, k_] := Sum[A[n, k - i]*(-1)^i*Binomial[k, i], {i, 0, k}];
a[n_] := T[n, 2];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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