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 A106440 #24 Apr 24 2025 08:50:48
%S A106440 1,30,420,4200,34650,252252,1681680,10501920,62355150,355655300,
%T A106440 1963217256,10546208400,55367594100,285028443000,1442592936000,
%U A106440 7193730107520,35406640372950,172255143129300,829376615067000
%N A106440 a(n) = binomial(2n+4,n)*binomial(n+4,4).
%C A106440 Fifth column of A104684.
%C A106440 Diagonal of the rational function 1 / (1 - x - y)^5. - _Ilya Gutkovskiy_, Apr 24 2025
%H A106440 Michael De Vlieger, <a href="/A106440/b106440.txt">Table of n, a(n) for n = 0..1642</a>
%H A106440 Ömür Deveci and Anthony G. Shannon, <a href="https://doi.org/10.20948/mathmontis-2021-50-4">Some aspects of Neyman triangles and Delannoy arrays</a>, Mathematica Montisnigri (2021) Vol. L, 36-43.
%F A106440 G.f.: (1+12x+6x^2)/(1-4x)^(9/2).
%F A106440 D-finite with recurrence n^2*a(n) -2*(n+2)*(2*n+3)*a(n-1)=0. - _R. J. Mathar_, Feb 20 2015
%F A106440 G.f.: 2F1(5/2,3;1;4x). - _R. J. Mathar_, Aug 09 2015
%F A106440 a(n) = A020920(n)+12*A020920(n-1)+6*A020920(n-2). - _R. J. Mathar_, Aug 09 2015
%F A106440 a(n) = (n+1)*A002803(n). - _R. J. Mathar_, Aug 09 2015
%t A106440 Table[Binomial[2n+4,n]Binomial[n+4,4],{n,0,20}] (* _Harvey P. Dale_, May 03 2019 *)
%Y A106440 Cf. A007744, A002544, A002457.
%Y A106440 Cf. A002803, A020920.
%K A106440 easy,nonn
%O A106440 0,2
%A A106440 _Paul Barry_, May 02 2005