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A261043 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. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
FORMULA
a(n) = A034899(n) - 2*A000041(n) + 1.
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...
MATHEMATICA
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];
Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Jun 01 2022, after Alois P. Heinz in A257740 *)
CROSSREFS
Column k=2 of A257740.
Sequence in context: A139263 A354507 A337075 * A063025 A187917 A164304
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Aug 08 2015
EXTENSIONS
New name from Alois P. Heinz, Oct 07 2018
STATUS
approved

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Last modified March 18 22:09 EDT 2024. Contains 370951 sequences. (Running on oeis4.)