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A084641
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Binomial transform of n^7.
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1
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0, 1, 130, 2574, 25904, 183200, 1040112, 5076400, 22171648, 88915968, 333209600, 1181548544, 4001402880, 13033885696, 41061830656, 125666611200, 374947708928, 1093874155520, 3128047828992, 8785866391552, 24280799641600, 66124498599936, 177683966197760
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OFFSET
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0,3
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COMMENTS
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The binomial transforms of n, n^2, n^3, n^4, n^5, n^6 are A001787, A001788, A058645, A058649, A059338, A056468 respectively.
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LINKS
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Table of n, a(n) for n=0..22.
Index entries for linear recurrences with constant coefficients, signature (16,-112,448,-1120,1792,-1792,1024,-256).
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FORMULA
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a(n) = n^2*(n^5+21*n^4+105*n^3+35*n^2 - 210*n+112)*2^(n-7).
a(n) = Sum_{k=0..n} C(n, k)*k^7.
G.f.: -x*(272*x^6-816*x^5+96*x^4+1168*x^3-606*x^2-114*x-1)/(2*x-1)^8. [Colin Barker, Sep 20 2012]
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MATHEMATICA
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LinearRecurrence[{16, -112, 448, -1120, 1792, -1792, 1024, -256}, {0, 1, 130, 2574, 25904, 183200, 1040112, 5076400}, 21] (* Amiram Eldar, Nov 26 2021 *)
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CROSSREFS
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Cf. A001015, A001787, A001788, A058645, A058649, A059338, A056468.
Sequence in context: A262108 A250212 A239094 * A271758 A228997 A168124
Adjacent sequences: A084638 A084639 A084640 * A084642 A084643 A084644
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry, Jun 08 2003
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STATUS
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approved
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