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.
%I A275944 #10 Aug 16 2016 12:32:16 %S A275944 1,1111,1122211,1123333211,1123445443211,1123456666543211, %T A275944 1123457788877543211,1123457901110987543211,1123457912334332087543211, %U A275944 1123457913456666543087543211,1123457913568899988653087543211,1123457913580123333209753087543211,1123457913581245667665420753087543211 %N A275944 Gaussian binomial coefficient [n,3] for q = 10. %C A275944 More generally, the ordinary generation function for the Gaussian binomial coefficients [n,k]_q is x^k/Product_{m=0..k} (1 - q^m*x). %C A275944 Convolution of A002275 and A147816 (considering offset: 0, 0, 1, 1100, 1110000, ...). %C A275944 The first seven members are palindromes. %H A275944 <a href="/index/Ga#Gaussian_binomial_coefficients">Index entries related to Gaussian binomial coefficients</a> %H A275944 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1111,-112110,1111000,-1000000) %F A275944 O.g.f.: x^3/((1 - x)*(1 - 10*x)*(1 - 100*x)*(1 - 1000*x)). %F A275944 E.g.f.: (-1000 + 1110*exp(9*x) - 111*exp(99*x) + exp(999*x))*exp(x)/890109000. %F A275944 a(n) = 1111*a(n-1) - 112110*a(n-2) + 1111000*a(n-3) - 1000000*a(n-4). %F A275944 a(n) = ((10^n - 100)*(10^n - 10)*(10^n - 1))/890109000. %F A275944 a(n) = Product_{i=0..2} (1 - 10^(n-i))/(1 - 10^(i+1)). %t A275944 Table[((10^n - 100) (10^n - 10) (10^n - 1))/890109000, {n, 0, 15}] %t A275944 Table[QBinomial[n, 3, 10], {n, 3, 15}] %Y A275944 Cf. A002275, A022174, A109242, A147816. %K A275944 nonn,easy %O A275944 3,2 %A A275944 _Ilya Gutkovskiy_, Aug 13 2016