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 A027810 a(n) = (n+1)*binomial(n+5, 5). 12
 1, 12, 63, 224, 630, 1512, 3234, 6336, 11583, 20020, 33033, 52416, 80444, 119952, 174420, 248064, 345933, 474012, 639331, 850080, 1115730, 1447160, 1856790, 2358720, 2968875, 3705156, 4587597, 5638528, 6882744, 8347680, 10063592, 12063744, 14384601, 17066028 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Number of 11-subsequences of [ 1, n ] with just 5 contiguous pairs. REFERENCES Albert H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196. Herbert John Ryser, Combinatorial Mathematics, Carus Mathematical Monographs No. 14, John Wiley and Sons, 1963, pp. 1-8. LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1). FORMULA G.f.: (1+5*x)/(1-x)^7. a(n) = A245334(n+5, 5)/A000142(5). - Reinhard Zumkeller, Aug 31 2014 From Amiram Eldar, Jan 28 2022: (Start) Sum_{n>=0} 1/a(n) = 5*Pi^2/6 - 1025/144. Sum_{n>=0} (-1)^n/a(n) = 5*Pi^2/12 - 160*log(2)/3 + 4865/144. (End) MAPLE [seq(n*(n-1)*(n-2)*(n-3)*(n-4)^2/5!, n=5..33)]; # Zerinvary Lajos, Oct 19 2006 MATHEMATICA Table[(n+1)Binomial[n+5, 5], {n, 0, 30}] (* Harvey P. Dale, Jul 29 2014 *) CoefficientList[Series[(1 + 5 x)/(1 - x)^7, {x, 0, 40}], x] (* Vincenzo Librandi, Jul 30 2014 *) PROG (Magma) [(n+1)*Binomial(n+5, 5): n in [0..40]] /* or */ [n*(n-1)*(n-2)*(n-3)*(n-4)^2/120: n in [5..40]]; // Vincenzo Librandi, Jul 30 2014 (Haskell) a027810 n = (n + 1) * a007318' (n + 5) 5 -- Reinhard Zumkeller, Aug 31 2014 (PARI) a(n)=n*(n^5+16*n^4+100*n^3+310*n^2+499*n+394)/120+1 \\ Charles R Greathouse IV, Sep 28 2015 CROSSREFS Partial sums of A051843. Cf. A093563 ((6, 1) Pascal, column m=6). Cf. A007318, A000142, A245334. Sequence in context: A309372 A085463 A051922 * A012875 A275404 A162472 Adjacent sequences: A027807 A027808 A027809 * A027811 A027812 A027813 KEYWORD nonn,easy AUTHOR Thi Ngoc Dinh (via R. K. Guy) EXTENSIONS Two redundant formulas deleted by N. J. A. Sloane, Jul 30 2014 STATUS approved

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Last modified April 18 08:27 EDT 2024. Contains 371769 sequences. (Running on oeis4.)