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 A027812 a(n) = 7*(n+1)*binomial(n+5,7). 1
 21, 224, 1260, 5040, 16170, 44352, 108108, 240240, 495495, 960960, 1769768, 3118752, 5290740, 8682240, 13837320, 21488544, 32605881, 48454560, 70662900, 101301200, 142972830, 198918720, 273136500, 370515600, 496989675, 659707776, 867225744, 1129719360, 1459220840 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 COMMENTS Number of 13-subsequences of [ 1, n ] with just 5 contiguous pairs. LINKS Harvey P. Dale, Table of n, a(n) for n = 2..1000 Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1). FORMULA G.f.: 7*(3+5x)*x^2/(1-x)^9. a(n) = C(n+1, 3)*C(n+5, 5). - Zerinvary Lajos, May 26 2005; corrected by R. J. Mathar, Feb 10 2016 From Amiram Eldar, Feb 04 2022: (Start) Sum_{n>=2} 1/a(n) = 5*Pi^2/2 - 5909/240. Sum_{n>=2} (-1)^n/a(n) = 5*Pi^2/4 - 32*log(2) + 791/80. (End) MATHEMATICA Table[7 * (n+1) * Binomial[n+5, 7], {n, 2, 50}] (* Amiram Eldar, Feb 04 2022 *) LinearRecurrence[{9, -36, 84, -126, 126, -84, 36, -9, 1}, {21, 224, 1260, 5040, 16170, 44352, 108108, 240240, 495495}, 30] (* Harvey P. Dale, Aug 01 2022 *) CROSSREFS Sequence in context: A134585 A165402 A135120 * A171112 A171108 A219439 Adjacent sequences: A027809 A027810 A027811 * A027813 A027814 A027815 KEYWORD nonn,easy AUTHOR Thi Ngoc Dinh (via R. K. Guy) STATUS approved

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Last modified September 29 12:01 EDT 2023. Contains 365771 sequences. (Running on oeis4.)