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A292845
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Total number of words beginning with the first letter of an n-ary alphabet in all sets of nonempty words with a total of n letters.
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3
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0, 1, 3, 28, 325, 4976, 92869, 2038842, 51397801, 1461081781, 46192638386, 1606531631321, 60921659773609, 2500525907856718, 110403919405245712, 5216038547426332891, 262495788417549517393, 14015335940464667636300, 791161963786588958170705
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OFFSET
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0,3
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LINKS
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EXAMPLE
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For n=2 and alphabet {a,b} we have 5 sets: {aa}, {ab}, {ba}, {bb}, {a,b}. There is a total of 3 words beginning with the first alphabet letter, thus a(2) = 3.
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MAPLE
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h:= proc(n, i, k) option remember; `if`(n=0, [1, 0], `if`(i<1, 0, add(
(p-> p+[0, p[1]*j])(binomial(k^i, j)*h(n-i*j, i-1, k)), j=0..n/i)))
end:
a= n-> `if`(n=0, 0, h(n$3)[2]/n):
seq(a(n), n=0..22);
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MATHEMATICA
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h[n_, i_, k_] := h[n, i, k] = If[n == 0, {1, 0}, If[i < 1, {0, 0}, Sum[ Function[p, p + {0, p[[1]]*j}][Binomial[k^i, j]*h[n - i*j, i - 1, k]], {j, 0, n/i}]]];
a[n_] := If[n == 0, 0, h[n, n, n][[2]]/n];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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