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 A070782 a(n) = Sum_{k=0..n} binomial(5*n,5*k). 16
 1, 2, 254, 6008, 215766, 6643782, 215492564, 6863694378, 219993856006, 7035859329512, 225191238869774, 7205634556190798, 230585685502492596, 7378682274243863442, 236118494435702913134, 7555784484021765207768, 241785184867484394069286, 7737125013254912900576822 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Seiichi Manyama, Table of n, a(n) for n = 0..664 Index entries for linear recurrences with constant coefficients, signature (21,353,-32). FORMULA a(n) = (1/5)*32^n + (2/5)*(-11/2 + (5/2)*sqrt(5))^n + (2/5)*(-11/2 - (5/2)*sqrt(5))^n. Let b(n) = a(n) - 2^(5n)/5; then b(n) + 11*b(n-1) - b(n-2) = 0. - Benoit Cloitre, May 27 2004 From Colin Barker, May 27 2019: (Start) G.f.: (1 - 19*x - 141*x^2) / ((1 - 32*x)*(1 + 11*x - x^2)). a(n) = 21*a(n-1) + 353*a(n-2) - 32*a(n-3) for n>2. (End) MATHEMATICA LinearRecurrence[{21, 353, -32}, {1, 2, 254}, 20] (* Harvey P. Dale, Jun 18 2023 *) PROG (PARI) a(n)=sum(k=0, n, binomial(5*n, 5*k)) (PARI) Vec((1 - 19*x - 141*x^2) / ((1 - 32*x)*(1 + 11*x - x^2)) + O(x^20)) \\ Colin Barker, May 27 2019 CROSSREFS Sum_{k=0..n} binomial(b*n,b*k): A000079 (b=1), A081294 (b=2), A007613 (b=3), A070775 (b=4), this sequence (b=5), A070967 (b=6), A094211 (b=7), A070832 (b=8), A094213 (b=9), A070833 (b=10). Sequence in context: A177320 A304211 A224828 * A078167 A004875 A067480 Adjacent sequences: A070779 A070780 A070781 * A070783 A070784 A070785 KEYWORD easy,nonn AUTHOR Sebastian Gutierrez and Sarah Kolitz (skolitz(AT)mit.edu), May 15 2002 STATUS approved

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Last modified September 21 18:57 EDT 2023. Contains 365503 sequences. (Running on oeis4.)