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A298104
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Number of connected dominating sets in the n-triangular graph.
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2
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1, 7, 54, 918, 31072, 2053184, 266478640, 68560228400, 35159451505536, 36021118923496320, 73782296097354062336, 302225812400352055040512, 2475866621867539032536216576, 40564755669895936890639118713856, 1329227401230786888692092742930946048
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OFFSET
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2,2
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LINKS
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FORMULA
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MATHEMATICA
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a[n_] := a[n] = 2^Binomial[n, 2] - Sum[k Binomial[n, k] 2^((n - k) (n - k - 1)/2) a[k], {k, n - 1}]/n; Join[{1}, Table[a[n] + n a[n - 1], {n, 3, 20}]] (* Eric W. Weisstein, Jan 15 2018 *)
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PROG
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(PARI)
b(n)={serlaplace(-x + log(sum(k=0, n, 2^binomial(k, 2)*x^k/k! + O(x*x^n))))}
{ my(n=20); Vec(b(n) + x*deriv(x*b(n))) } \\ Andrew Howroyd, Jan 14 2018
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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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