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 A176203 #8 Sep 08 2022 08:45:52
%S A176203 1,1,1,1,17,1,1,33,33,1,1,49,81,49,1,1,65,145,145,65,1,1,81,225,305,
%T A176203 225,81,1,1,97,321,545,545,321,97,1,1,113,433,881,1105,881,433,113,1,
%U A176203 1,129,561,1329,2001,2001,1329,561,129,1,1,145,705,1905,3345,4017,3345,1905,705,145,1
%N A176203 Triangle read by rows: T(n, k) = 16*binomial(n, k) - 15.
%C A176203 This sequence belongs to the class defined by T(n, m, q) = 2*T(n, m, q-1) - 1. The first few q values gives the sequences: A007318 (q=0), A109128 (q=1), A131061 (q=2), A168625 (q=3), this sequence (q=4).
%C A176203 Row sums are: {1, 2, 19, 68, 181, 422, 919, 1928, 3961, 8042, 16219, ...}.
%C A176203 Former title: A recursive symmetrical triangular sequence:q=4: t(n, m, q) = 2*t(n, m, q-1) - 1. - _G. C. Greubel_, Mar 12 2020
%H A176203 G. C. Greubel, <a href="/A176203/b176203.txt">Rows n = 0..100 of the triangle, flattened</a>
%F A176203 T(n, m, q) = 2*T(n, m, q-1) - 1, with T(n, m, 0) = binomial(n, m) and q = 4.
%F A176203 From _G. C. Greubel_, Mar 12 2020: (Start)
%F A176203 T(n, k, q) = 2^q * binomial(n, k) - (2^q - 1), with q = 4.
%F A176203 Sum_{k=0..n} T(n, k, q) = 2^(n + q) - (n + 1)*(2^q - 1) (row sums). (End)
%e A176203 Triangle begins as:
%e A176203 1;
%e A176203 1, 1;
%e A176203 1, 17, 1;
%e A176203 1, 33, 33, 1;
%e A176203 1, 49, 81, 49, 1;
%e A176203 1, 65, 145, 145, 65, 1;
%e A176203 1, 81, 225, 305, 225, 81, 1;
%e A176203 1, 97, 321, 545, 545, 321, 97, 1;
%e A176203 1, 113, 433, 881, 1105, 881, 433, 113, 1;
%e A176203 1, 129, 561, 1329, 2001, 2001, 1329, 561, 129, 1;
%e A176203 1, 145, 705, 1905, 3345, 4017, 3345, 1905, 705, 145, 1;
%p A176203 A176203:= (n,k) -> 16*binomial(n, k) -15; seq(seq(A176203(n, k), k = 0..n), n = 0.. 12); # _G. C. Greubel_, Mar 12 2020
%t A176203 T[n_, m_, q]:= 2^q*(Binomial[n, m] -1) + 1; Table[T[n,m,4], {n,0,12}, {m,0,n} ]//Flatten (* modified by _G. C. Greubel_, Mar 12 2020 *)
%t A176203 Table[16*Binomial[n, k] -15, {n,0,12}, {k,0,n}]//Flatten (* _G. C. Greubel_, Mar 12 2020 *)
%o A176203 (Magma) [16*Binomial(n, k) -15: k in [0..n], n in [0..12]]; // _G. C. Greubel_, Mar 12 2020
%o A176203 (Sage) [[16*binomial(n, k) -15 for k in (0..n)] for n in (0..12)] # _G. C. Greubel_, Mar 12 2020
%Y A176203 Sequence m*binomial(n,k) - (m-1): A007318 (m=1), this sequence (m=2), A131060 (m=3), A131061 (m=4), A131063 (m=5), A131065 (m=6), A131067 (m=7), A168625 (m=8), this sequence (m=16).
%K A176203 nonn,tabl
%O A176203 0,5
%A A176203 _Roger L. Bagula_, Apr 11 2010
%E A176203 Edited by _G. C. Greubel_, Mar 12 2020