A027775 a(n) = (n+1)*binomial(n+1, 15).

15, 256, 2312, 14688, 73644, 310080, 1139544, 3751968, 11277222, 31380096, 81719000, 200880160, 469364220, 1048380480, 2249204040, 4653525600, 9316746045, 18103127040, 34226224560, 63102895680, 113678010600, 200444492160, 346475391120, 587908889280

Offset: 14

Author

Thi Ngoc Dinh (via R. K. Guy)

Keywords

• nonn

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).

Programs

Magma

[(n+1)*Binomial(n+1, 15): n in [14..30]]; // Vincenzo Librandi, Jul 27 2011

Mathematica

Table[(n+1)Binomial[n+1,15],{n,14,40}] (* Harvey P. Dale, Jul 26 2011 *)

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)

Extensions

Offset corrected by Harvey P. Dale, Jul 26 2011