A027766 a(n) = (n+1)*binomial(n+1,6).

6, 49, 224, 756, 2100, 5082, 11088, 22308, 42042, 75075, 128128, 210392, 334152, 515508, 775200, 1139544, 1641486, 2321781, 3230304, 4427500, 5985980, 7992270, 10548720, 13775580, 17813250, 22824711, 28998144, 36549744, 45726736, 56810600, 70120512, 86017008

Offset: 5

Author

Thi Ngoc Dinh (via R. K. Guy)

Keywords

• nonn
• easy

Comments

Number of 8-subsequences of [ 1, n ] with just 1 contiguous pair.

36*a(n) is the number of permutations of (n+1) symbols that 6-commute with an (n+1)-cycle (see A233440 for definition), where 36 = A000757(6). - Luis Manuel Rivera Martínez, 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 (8,-28,56,-70,56,-28,8,-1).

Crossrefs

Cf. A000757, A233440.

Formula

G.f.: (6+x)*x^5/(1-x)^8.

From Amiram Eldar, Jan 30 2022: (Start)

Sum_{n>=5} 1/a(n) = 3019/300 - Pi^2.

Sum_{n>=5} (-1)^(n+1)/a(n) = Pi^2/2 + 512*log(2)/5 - 22729/300. (End)