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 A265890 #23 Jul 08 2018 01:36:25 %S A265890 1,1,0,1,1,0,1,1,1,0,1,1,1,1,0,1,2,2,1,1,0,1,2,3,2,1,1,0,1,1,1,1,3,1, %T A265890 1,0,1,1,1,1,1,3,1,1,0,1,1,2,2,2,1,4,1,1,0,1,1,3,4,4,3,1,4,1,1,0,1,1, %U A265890 3,1,1,6,3,1,5,1,1,0,1,1,4,1,1,1,8,4,1,5,1,1,0,1,2,1,1,2,2,1,1,5,2,6,1,1,0,1,2,1,2,3,3,3,2,1,6,2,6,1,1,0 %N A265890 Array read by ascending antidiagonals: A(n,k) = A099563(A265609(n,k)), with n as row >= 0, k as column >= 0; the most significant digit in the factorial base representation of rising factorial n^(k) = (n+k-1)!/(n-1)!. %C A265890 Square array A(row,col) is read by ascending antidiagonals as: A(0,0), A(1,0), A(0,1), A(2,0), A(1,1), A(0,2), A(3,0), A(2,1), A(1,2), A(0,3), ... %C A265890 A265609(n,k) is the rising factorial, also known as Pochhammer symbol and A099563(n) is the most significant "digit" (place holder) in the factorial representation (A007623) of n. %H A265890 Antti Karttunen, <a href="/A265890/b265890.txt">Table of n, a(n) for n = 0..7259; the first 120 antidiagonals of array</a> %H A265890 <a href="/index/Fa#facbase">Index entries for sequences related to factorial base representation</a> %e A265890 The top left corner of the array A265609 with its terms shown in factorial base (A007623) looks like this: %e A265890 1, 0, 0, 0, 0, 0, 0, 0, 0 %e A265890 1, 1, 10, 100, 1000, 10000, 100000, 1000000, 10000000 %e A265890 1, 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000 %e A265890 1, 11, 200, 2200, 30000, 330000, 4000000, 44000000, 500000000 %e A265890 1, 20, 310, 10000, 110000, 1220000, 14000000, 160000000, 1830000000 %e A265890 1, 21, 1100, 13300, 220000, 3000000, 36000000, 452000000, 5500000000 %e A265890 1, 100, 1300, 24000, 411000, 6000000, 82000000, 1100000000, 13300000000 %e A265890 1, 101, 2110, 41000, 1000000, 13000000, 174000000, 2374000000, 30360000000 %e A265890 - %e A265890 Taking the most significant "digit" (placeholder that may get arbitrarily large values) gives us the top left corner of this array: %e A265890 - %e A265890 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 %e A265890 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 %e A265890 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 %e A265890 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11 %e A265890 1, 2, 3, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3 %e A265890 1, 2, 1, 1, 2, 3, 3, 4, 5, 6, 7, 8, 10, 11, 12, 14, 15, 17, 19, 21, 1 %e A265890 1, 1, 1, 2, 4, 6, 8, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 4, 4, 5 %e A265890 1, 1, 2, 4, 1, 1, 1, 2, 3, 3, 4, 5, 6, 8, 9, 11, 12, 14, 16, 19, 21 %e A265890 1, 1, 3, 1, 1, 2, 3, 4, 6, 8, 11, 14, 1, 1, 1, 1, 2, 2, 2, 3, 3 %e A265890 1, 1, 3, 1, 2, 3, 5, 8, 1, 1, 1, 2, 2, 3, 4, 5, 6, 7, 8, 10, 12 %e A265890 1, 1, 4, 1, 3, 5, 9, 1, 2, 2, 3, 5, 6, 8, 11, 14, 17, 21, 1, 1, 1 %e A265890 1, 1, 1, 2, 4, 8, 1, 2, 3, 5, 7, 10, 14, 1, 1, 1, 2, 2, 3, 3, 4 %e A265890 1, 2, 1, 3, 6, 1, 2, 4, 6, 9, 14, 1, 1, 2, 3, 4, 5, 6, 8, 10, 13 %e A265890 1, 2, 1, 3, 1, 2, 3, 6, 10, 1, 1, 2, 3, 5, 6, 9, 12, 16, 21, 1, 1 %e A265890 1, 2, 1, 4, 1, 2, 5, 9, 1, 2, 3, 4, 7, 10, 14, 20, 1, 1, 2, 2, 3 %e A265890 1, 2, 2, 5, 1, 3, 7, 1, 2, 3, 5, 8, 13, 1, 1, 1, 2, 3, 4, 6, 8 %e A265890 ... %o A265890 (Scheme) %o A265890 (define (A265890 n) (A265890bi (A025581 n) (A002262 n))) %o A265890 (define (A265890bi row col) (A099563 (A265609bi row col))) ;; Code for A265609bi given in A265609. %Y A265890 Cf. A007623, A265609. %Y A265890 Column 1: A099563. %Y A265890 Row 0: A000007, rows 1 & 2: A000012, row 3: A008619 (see comment in A001710). %Y A265890 Row 4: 1,2,3 followed by A097992 ? %Y A265890 Main diagonal: A265891 (essentially, without the initial 1 from the corner of this array). %Y A265890 Cf. also array A265892. %K A265890 nonn,tabl %O A265890 0,17 %A A265890 _Antti Karttunen_, Dec 19 2015