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 A027764 a(n) = (n+1)*binomial(n+1,4). 2
 4, 25, 90, 245, 560, 1134, 2100, 3630, 5940, 9295, 14014, 20475, 29120, 40460, 55080, 73644, 96900, 125685, 160930, 203665, 255024, 316250, 388700, 473850, 573300, 688779, 822150, 975415, 1150720, 1350360, 1576784, 1832600 (list; graph; refs; listen; history; text; internal format)
 OFFSET 3,1 COMMENTS a(n) is also the number of permutations of n+1 symbols that 4-commute with an (n+1)-cycle (see A233440 for definition). - Luis Manuel Rivera MartÃ­nez, Feb 07 2014 LINKS Vincenzo Librandi, Table of n, a(n) for n = 3..1000 Luis Manuel Rivera, Integer sequences and k-commuting permutations, arXiv preprint arXiv:1406.3081, 2014 Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1). FORMULA Number of 6-subsequences of [ 1, n ] with just 1 contiguous pair; g.f. (4+x)*x^3/(1-x)^6. a(3)=4, a(4)=25, a(5)=90, a(6)=245, a(7)=560, a(8)=1134, a(n)=6*a(n-1) -15*a(n-2)+20*a(n-3)-15*a(n-4)+6*a(n-5)-a(n-6). - Harvey P. Dale, Jun 14 2013 a(n) = 10*C(n+2,2)*C(n+2,5)/(n+2)^2. - Gary Detlefs, Aug 20 2013 Sum_{n>=3} 1/a(n) = 62/9 - 2/3*Pi^2. - Jaume Oliver Lafont, Jul 15 2017 MATHEMATICA Table[(n + 1)Binomial[n + 1, 4], {n, 3, 40}] (* or *) LinearRecurrence[ {6, -15, 20, -15, 6, -1}, {4, 25, 90, 245, 560, 1134}, 40] (* Harvey P. Dale, Jun 14 2013 *) CoefficientList[Series[(4 + x)/(1 - x)^6, {x, 0, 30}], x] (* Vincenzo Librandi, Feb 08 2014 *) PROG (MAGMA) [(n+1)*Binomial(n+1, 4): n in [3..35]]; // Vincenzo Librandi, Feb 08 2014 CROSSREFS Cf. A233440. Sequence in context: A266126 A303514 A041991 * A095669 A323967 A195509 Adjacent sequences:  A027761 A027762 A027763 * A027765 A027766 A027767 KEYWORD nonn,easy AUTHOR Thi Ngoc Dinh (via R. K. Guy) STATUS approved

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Last modified October 14 16:48 EDT 2019. Contains 328022 sequences. (Running on oeis4.)