A027770 a(n) = (n + 1)*binomial(n + 1, 10).

10, 121, 792, 3718, 14014, 45045, 128128, 330616, 787644, 1755182, 3695120, 7407036, 14226212, 26313518, 47070144, 81719000, 138105110, 227779695, 367447080, 580870290, 901350450, 1374917115, 2064391680, 3054514320, 4458356760, 6425278860, 9150726816

Offset: 9

Author

Thi Ngoc Dinh (via R. K. Guy)

Keywords

• nonn
• easy

Comments

Number of 12-subsequences of [ 1, n ] with just one contiguous pair.

120288*a(n) is the number of permutations of (n+1) symbols that 10-commute with an (n+1)-cycle (see A233440 for definition), where 120288 = A000757(10). - Luis Manuel Rivera Martínez, Feb 07 2014

Links

• T. D. Noe, Table of n, a(n) for n = 9..1000
• 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 (12,-66,220,-495,792,-924,792,-495,220,-66,12,-1).

Crossrefs

Cf. A000757, A233440.

Programs

Maple

a:= n-> (n+1)*binomial(n+1, 10):
seq(a(n), n=9..36);  # Alois P. Heinz, Oct 04 2019

Mathematica

((# + 1) Binomial[# + 1, 10] &) /@ Range[9, 48] (* Alonso del Arte, Oct 04 2019 *)

Formula

G.f.: (10 + x)*x^9/(1 - x)^12.

a(n) = C(n + 1, 10)*C(n + 1, 1). - Zerinvary Lajos, Jun 08 2005, corrected by R. J. Mathar, Feb 13 2016

From Amiram Eldar, Jan 30 2022: (Start)

Sum_{n>=9} 1/a(n) = 5257891/317520 - 5*Pi^2/3.

Sum_{n>=9} (-1)^(n+1)/a(n) = 5*Pi^2/6 + 84992*log(2)/63 - 299498341/317520. (End)