OFFSET
14,1
COMMENTS
Number of 17-subsequences of [ 1, n ] with just 1 contiguous pair.
LINKS
Vincenzo Librandi and T. D. Noe, Table of n, a(n) for n = 14..1000 (first 300 terms from Vincenzo Librandi)
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 (17,-136,680,-2380,6188,-12376,19448,-24310,24310,-19448,12376,-6188,2380,-680,136,-17,1).
FORMULA
G.f.: x^14*(15+x)/(1-x)^17.
From Amiram Eldar, Jan 30 2022: (Start)
Sum_{n>=14} 1/a(n) = 5*Pi^2/2 - 106497287263/4328644320.
Sum_{n>=14} (-1)^n/a(n) = 5*Pi^2/4 + 115552256*log(2)/3003 - 16500694723831/618377760. (End)
MATHEMATICA
Table[(n+1)Binomial[n+1, 15], {n, 14, 40}] (* Harvey P. Dale, Jul 26 2011 *)
PROG
(Magma) [(n+1)*Binomial(n+1, 15): n in [14..30]]; // Vincenzo Librandi, Jul 27 2011
CROSSREFS
KEYWORD
nonn
AUTHOR
Thi Ngoc Dinh (via R. K. Guy)
EXTENSIONS
Offset corrected by Harvey P. Dale, Jul 26 2011
STATUS
approved