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 A147724 #21 Mar 16 2025 02:35:06
%S A147724 1,1,1,4,5,1,25,33,9,1,172,238,78,13,1,1201,1745,667,139,17,1,8404,
%T A147724 12807,5583,1376,216,21,1,58825,93841,45822,12950,2429,309,25,1,
%U A147724 411772,686288,370108,117458,25366,3890,418,29,1,2882401,5009889,2951034,1035834,251583,44607,5823,543,33,1
%N A147724 a(n) = C(3,n) DELTA C(0,n).
%C A147724 Triangle [1,3,3,1,0,0,0,...] DELTA [1,0,0,0,...] with Deléham DELTA as in A084938.
%C A147724 First column is A034494(n-1). Row sums are A147725. A147724 = A147723*A007318.
%H A147724 Indranil Ghosh, <a href="/A147724/b147724.txt">Rows 0..100, flattened</a>
%F A147724 Riordan array ((1-7*x+3*x^2)/(1-8*x+7*x^2), x*(1-4*x)/(1-8*x+7*x^2)).
%F A147724 G.f.: (1 - 7*x + 3*x^2)/(1 - 8*x + 7*x^2 - x*y + 4*x^2*y). - _Philippe Deléham_, Oct 29 2013
%F A147724 T(n,k) = 8*T(n-1,k) + T(n-1,k-1) - 7*T(n-2,k) - 4*T(n-2,k-1), T(0,0) = T(1,0) = T(1,1) = T(2,2) = 1, T(2,0) = 4, T(2,1) = 5, T(n,k) = 0 if k > n or if k < 0. - _Philippe Deléham_, Oct 29 2013
%e A147724 Triangle begins
%e A147724 1;
%e A147724 1, 1;
%e A147724 4, 5, 1;
%e A147724 25, 33, 9, 1;
%e A147724 172, 238, 78, 13, 1;
%t A147724 nmax=9; Flatten[CoefficientList[Series[CoefficientList[Series[(1 - 7*x + 3*x^2)/(1 - 8*x + 7*x^2 - x*y + 4*x^2*y) , {x, 0, nmax}], x], {y, 0, nmax}], y]] (* _Indranil Ghosh_, Mar 10 2017 *)
%Y A147724 Cf. A147721.
%K A147724 easy,nonn,tabl
%O A147724 0,4
%A A147724 _Paul Barry_, Nov 11 2008