OFFSET
7,1
COMMENTS
Number of 10-subsequences of [ 1, n ] with just 1 contiguous pair.
1625*a(n) is the number of permutations of (n+1) symbols that 8-commute with an (n+1)-cycle (see A233440 for definition), where 1625 = A000757(8). - Luis Manuel Rivera MartÃnez, Feb 07 2014
LINKS
Luis Manuel Rivera, Integer sequences and k-commuting permutations, arXiv preprint arXiv:1406.3081 [math.CO], 2014-2015.
Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).
FORMULA
G.f.: (8+x)*x^7/(1-x)^10.
From Amiram Eldar, Jan 30 2022: (Start)
Sum_{n>=7} 1/a(n) = 48877/3675 - 4*Pi^2/3.
Sum_{n>=7} (-1)^(n+1)/a(n) = 2*Pi^2/3 + 38656*log(2)/105 - 2884681/11025. (End)
MATHEMATICA
Table[(n+1)Binomial[n+1, 8], {n, 7, 40}] (* Harvey P. Dale, Jul 08 2017 *)
PROG
(PARI) a(n) = (n+1)*binomial(n+1, 8); \\ Michel Marcus, Jan 31 2014
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Thi Ngoc Dinh (via R. K. Guy)
EXTENSIONS
Incorrect formula deleted . - R. J. Mathar, Feb 13 2016
STATUS
approved