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A006129
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a(0),a(1),a(2),... satisfy Sum a(k) binomial(n,k) (k=0..n) = 2^binomial(n,2), for n=0,1,...
(Formerly M3678)
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10
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1, 0, 1, 4, 41, 768, 27449, 1887284, 252522481, 66376424160, 34509011894545, 35645504882731588, 73356937912127722841, 301275024444053951967648, 2471655539737552842139838345, 40527712706903544101000417059892
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| Also labeled graphs on n unisolated nodes (inverse binomial transform of A006125).
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REFERENCES
| N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| N. J. A. Sloane, Transforms
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FORMULA
| a(n) = sum_{k=0..n} (-1)^(n-k)*binomial(n, k)*2^binomial(k, 2).
E.g.f.: A(x)/exp(x) where A(x) = Sum_{n>=0} 2^binomial(n,2) x^n/n!. (*Geoffrey Critzer, Oct 21 2011*)
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EXAMPLE
| 2^binomial(n,2) = 1 + binomial(n,2) + 4*binomial(n,3) + 41*binomial(n,4) + 768*binomial(n,5)+...
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MATHEMATICA
| a=Sum[2^Binomial[n, 2] x^n/n!, {n, 0, 20}]; Range[0, 20]!CoefficientList[Series[ a/Exp[x], {x, 0, 20}], x]
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CROSSREFS
| Sequence in context: A085340 A001908 A192547 * A022515 A172496 A059730
Adjacent sequences: A006126 A006127 A006128 * A006130 A006131 A006132
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KEYWORD
| nonn,nice,easy
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AUTHOR
| C. L. Mallows (colinm(AT)research.avayalabs.com)
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EXTENSIONS
| More terms and additional comments from Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 09 2000
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