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A085442
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a(n) = Sum_{i=1..n} binomial(i+1,2)^7.
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25
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1, 2188, 282124, 10282124, 181141499, 1982230040, 15475158552, 93839322648, 467508775773, 1989944010148, 7445104711204, 25010673566116, 76686775501847, 217396817767472, 575714897767472, 1436257466526768, 3398894618986905, 7674255436599996, 16612972826599996
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OFFSET
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1,2
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (16,-120,560,-1820,4368,-8008,11440,-12870,11440,-8008,4368,-1820,560,-120,16,-1).
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FORMULA
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a(n) = (1/823680) *n*(n+1)*(n+2)*(429*n^12 +5148*n^11 +24123*n^10 +52470*n^9 +43047*n^8 -8856*n^7 +4109*n^6 +50430*n^5 -18796*n^4 -44472*n^3 +26864*n^2 +8352*n -5568). - Vladeta Jovovic, Jul 07 2003
G.f.: x*(x^12 +2172*x^11 +247236*x^10 +6030140*x^9 +49258935*x^8 +163809288*x^7 +242384856*x^6 +163809288*x^5 +49258935*x^4 +6030140*x^3 +247236*x^2 +2172*x+ 1) / (x -1)^16. - Colin Barker, May 02 2014
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MATHEMATICA
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Table[Sum[Binomial[k+1, 2]^7, {k, 1, n}], {n, 1, 30}] (* G. C. Greubel, Nov 22 2017 *)
LinearRecurrence[{16, -120, 560, -1820, 4368, -8008, 11440, -12870, 11440, -8008, 4368, -1820, 560, -120, 16, -1}, {1, 2188, 282124, 10282124, 181141499, 1982230040, 15475158552, 93839322648, 467508775773, 1989944010148, 7445104711204, 25010673566116, 76686775501847, 217396817767472, 575714897767472, 1436257466526768}, 20] (* Harvey P. Dale, May 11 2022 *)
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PROG
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(PARI) for(n=1, 30, print1(sum(k=1, n, binomial(k+1, 2)^7), ", ")) \\ G. C. Greubel, Nov 22 2017
(Magma) [(1/823680) *n*(n+1)*(n+2)*(429*n^12 +5148*n^11 +24123*n^10 +52470*n^9 +43047*n^8 -8856*n^7 +4109*n^6 +50430*n^5 -18796*n^4 -44472*n^3 +26864*n^2 +8352*n -5568): n in [1..30]]; // G. C. Greubel, Nov 22 2017
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CROSSREFS
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Cf. A000292, A087127, A024166, A024166, A085438, A085439, A085440, A085441, A000332, A086020, A086021, A086022, A000389, A086023, A086024, A000579, A086025, A086026, A000580, A086027, A086028, A027555, A086029, A086030.
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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