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 A355664 #4 Jul 14 2022 09:35:26
%S A355664 0,0,0,0,1,0,0,2,2,0,0,3,9,3,0,0,4,12,12,4,0,0,5,35,15,35,5,0,0,6,38,
%T A355664 48,48,38,6,0,0,7,49,51,271,51,49,7,0,0,8,56,60,284,284,60,56,8,0,0,9,
%U A355664 135,63,387,313,387,63,135,9,0,0,10,142,192,448,398,398,448,192,142,10,0
%N A355664 Square array A(n, k), n, k >= 0, read by antidiagonals; for any number n with runs in binary expansion (r_w, ..., r_0), let p(n) be the polynomial of a single indeterminate x where the coefficient of x^e is r_e for e = 0..w and otherwise 0, and let q be the inverse of p; A(n, k) = q(p(n) * p(k)).
%C A355664 In other words, A(n, k) encodes the product of the polynomials encoded by n and k.
%H A355664 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F A355664 A(n, k) = A(k, n).
%F A355664 A(n, 0) = 0.
%F A355664 A(n, 1) = n.
%F A355664 A(n, 3) = A001196(n).
%F A355664 A(n, 7) = A097254(n+1).
%F A355664 A(n, n) = A355654(n).
%e A355664 Array A(n, k) begins:
%e A355664 n\k| 0 1 2 3 4 5 6 7 8 9 10 11
%e A355664 ---+---------------------------------------------------------------------
%e A355664 0| 0 0 0 0 0 0 0 0 0 0 0 0
%e A355664 1| 0 1 2 3 4 5 6 7 8 9 10 11
%e A355664 2| 0 2 9 12 35 38 49 56 135 142 153 156
%e A355664 3| 0 3 12 15 48 51 60 63 192 195 204 207
%e A355664 4| 0 4 35 48 271 284 387 448 2111 2172 2275 2288
%e A355664 5| 0 5 38 51 284 313 398 455 2168 2289 2502 2531
%e A355664 6| 0 6 49 60 387 398 481 504 3079 3102 3185 3196
%e A355664 7| 0 7 56 63 448 455 504 511 3584 3591 3640 3647
%e A355664 8| 0 8 135 192 2111 2168 3079 3584 33279 33784 34695 34752
%e A355664 9| 0 9 142 195 2172 2289 3102 3591 33784 34785 36622 36739
%e A355664 10| 0 10 153 204 2275 2502 3185 3640 34695 36622 39993 40476
%e A355664 11| 0 11 156 207 2288 2531 3196 3647 34752 36739 40476 40719
%e A355664 12| 0 12 195 240 3087 3132 3843 4032 49215 49404 50115 50160
%o A355664 (PARI) toruns(n) = { my (r=[]); while (n, my (v=valuation(n+n%2, 2)); n\=2^v; r=concat(v, r)); r }
%o A355664 fromruns(r) = { my (v=0); for (k=1, #r, v=(v+k%2)*2^r[k]-k%2); v }
%o A355664 A(n,k) = { fromruns(Vec(Pol(toruns(n)) * Pol(toruns(k)))) }
%Y A355664 Cf. A001196, A097254, A101211, A355663.
%K A355664 nonn,base,tabl
%O A355664 0,8
%A A355664 _Rémy Sigrist_, Jul 13 2022