cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A027775 #46 Jan 30 2022 04:17:11
%S A027775 15,256,2312,14688,73644,310080,1139544,3751968,11277222,31380096,
%T A027775 81719000,200880160,469364220,1048380480,2249204040,4653525600,
%U A027775 9316746045,18103127040,34226224560,63102895680,113678010600,200444492160,346475391120,587908889280
%N A027775 a(n) = (n+1)*binomial(n+1, 15).
%C A027775 Number of 17-subsequences of [ 1, n ] with just 1 contiguous pair.
%H A027775 Vincenzo Librandi and T. D. Noe, <a href="/A027775/b027775.txt">Table of n, a(n) for n = 14..1000</a> (first 300 terms from Vincenzo Librandi)
%H A027775 Luis Manuel Rivera, <a href="http://arxiv.org/abs/1406.3081">Integer sequences and k-commuting permutations</a>, arXiv preprint arXiv:1406.3081 [math.CO], 2014-2015.
%H A027775 <a href="/index/Rec#order_17">Index entries for linear recurrences with constant coefficients</a>, signature (17,-136,680,-2380,6188,-12376,19448,-24310,24310,-19448,12376,-6188,2380,-680,136,-17,1).
%F A027775 G.f.: x^14*(15+x)/(1-x)^17.
%F A027775 From _Amiram Eldar_, Jan 30 2022: (Start)
%F A027775 Sum_{n>=14} 1/a(n) = 5*Pi^2/2 - 106497287263/4328644320.
%F A027775 Sum_{n>=14} (-1)^n/a(n) = 5*Pi^2/4 + 115552256*log(2)/3003 - 16500694723831/618377760. (End)
%t A027775 Table[(n+1)Binomial[n+1,15],{n,14,40}] (* _Harvey P. Dale_, Jul 26 2011 *)
%o A027775 (Magma) [(n+1)*Binomial(n+1, 15): n in [14..30]]; // _Vincenzo Librandi_, Jul 27 2011
%K A027775 nonn
%O A027775 14,1
%A A027775 Thi Ngoc Dinh (via _R. K. Guy_)
%E A027775 Offset corrected by _Harvey P. Dale_, Jul 26 2011