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 A034942 #15 Jul 08 2025 21:28:36
%S A034942 1,6,32,163,813,4013,19703,96477,471811,2306316,11274066,55128021,
%T A034942 269688723,1320047550,6465047880,31682288305,155354522955,
%U A034942 762235643450,3742013092520,18380748447345,90334417334095,444186621323945,2185193308168959,10755153057295603,52958560495897573
%N A034942 Binomial transform of A002054.
%H A034942 Vincenzo Librandi, <a href="/A034942/b034942.txt">Table of n, a(n) for n = 0..1000</a>
%H A034942 László Németh, <a href="https://arxiv.org/abs/1905.13475">Tetrahedron trinomial coefficient transform</a>, arXiv:1905.13475 [math.CO], 2019.
%F A034942 Recurrence: (n+3)*(3*n+1)*a(n) = 3*(6*n^2+15*n+11)*a(n-1) - 5*(n-1)*(3*n+4)*a(n-2). - _Vaclav Kotesovec_, Oct 08 2012
%F A034942 a(n) ~ 4*5^(n+1/2)/sqrt(Pi*n). - _Vaclav Kotesovec_, Oct 08 2012
%t A034942 Table[Sum[Binomial[n,k]*Binomial[2*k+3,k],{k,0,n}],{n,0,25}] (* _Vaclav Kotesovec_, Oct 08 2012 *)
%o A034942 (PARI) a(n)=sum(k=0,n,binomial(n,k)*binomial(2*k+3,k)); \\ _Joerg Arndt_, May 04 2013
%K A034942 nonn,easy
%O A034942 0,2
%A A034942 _N. J. A. Sloane_