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 A102473 #7 Sep 14 2014 14:48:32 %S A102473 1,1,1,1,2,3,1,3,7,10,1,4,13,30,43,1,5,21,68,157,225,1,6,31,130,421, %T A102473 972,1393,1,7,43,222,931,3015,6961,9976,1,8,57,350,1807,7578,24541, %U A102473 56660,81201,1,9,73,520,3193,16485,69133,223884,516901,740785,1,10,91,738 %N A102473 Triangle read by rows. Let S(k) be the sequence defined by F(0)=0, F(1)=1, F(n-1) + (n+k)*F(n) = F(n+1). E.g. S(0) = 0,1,1,3,10,43,225,1393,9976,81201, ... Then S(0), S(1), S(2), ... are written next to each other, vertically, with the initial term of each on the next row down. The order of the terms in the rows are then reversed. %C A102473 For this triangle, the algorithm that generates the Bernoulli numbers gives 3/2, then 1/6, 1/24, ... 1/n! %C A102473 T(n,n) = A001040(n); T(n,k) = A058294(n,k), k = 1..n. - _Reinhard Zumkeller_, Sep 14 2014 %H A102473 Reinhard Zumkeller, <a href="/A102473/b102473.txt">Rows n = 1..125 of triangle, flattened</a> %e A102473 Triangle begins: %e A102473 0 %e A102473 0 1 %e A102473 0 1 1 %e A102473 0 1 2 3 %e A102473 0 1 3 7 10 %e A102473 0 1 4 13 30 43 %e A102473 ... %e A102473 (the zeros are omitted). %o A102473 (Haskell) %o A102473 a102473 n k = a102473_tabl !! (n-1) !! (k-1) %o A102473 a102473_row n = a102473_tabl !! (n-1) %o A102473 a102473_tabl = [1] : [1, 1] : f [1] [1, 1] 2 where %o A102473 f us vs x = ws : f vs ws (x + 1) where %o A102473 ws = 1 : zipWith (+) ([0] ++ us) (map (* x) vs) %o A102473 -- _Reinhard Zumkeller_, Sep 14 2014 %Y A102473 Mirror image of triangle in A102472. %Y A102473 Cf. A001040, A058294, A247365 (central terms). %K A102473 easy,nonn,tabl %O A102473 1,5 %A A102473 Russell Walsmith (russw(AT)lycos.com), Jan 09 2005 %E A102473 Entry revised by _N. J. A. Sloane_, Jul 09 2005