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 A136205 #13 Jan 30 2025 05:22:17
%S A136205 1,1,2,1,10,24,1,22,252,720,1,38,892,12176,40320,1,58,2232,60336,
%T A136205 966240,3628800,1,82,4632,199440,6202080,114341760,479001600,1,110,
%U A136205 8524,526256,25598016,905049216,18897709824,87178291200,1,142,14412,1197360
%N A136205 Square array read by antidiagonals: T(m,n) = H(n,2*m)*(2*m)!/(2*m+2*n-1). H(0,m) = 1/m, for all positive integers m. H(n,m) = Sum_{k=1..m} H(n-1,k).
%C A136205 In the array, the first m is 1; the first n is 0.
%C A136205 Every term of the array is a positive integer.
%F A136205 For n>=1, T(m,n) also equals (H(2*m+n-1) - H(n-1)) * (2*m+n-1)!/((2*m+2*n-1)*(n-1)!), where H(k) = H(1,k), the k-th harmonic number.
%e A136205 Array: (The upper-leftmost term is T(1,0).)
%e A136205 1, 2, 24, 720 (Row equals {(2*m-2)!}.)
%e A136205 1, 10, 252 (Row equals {H(1,2*m)*(2*m)!/(2*m+1)}, where H(1,2*m) = the (2*m)th harmonic number.)
%e A136205 1, 22 (Row equals {H(2,2*m)*(2*m)!/(2*m+3)}.)
%e A136205 1 (Row equals {H(3,2*m)*(2*m)!/(2*m+5)}.)
%e A136205 The column {T(1,n)} consists entirely of 1's.
%Y A136205 Cf. A105954.
%Y A136205 Cf. A090288, A010050, A114450.
%K A136205 nonn,tabl
%O A136205 0,3
%A A136205 _Leroy Quet_, Mar 16 2008
%E A136205 More terms from _R. J. Mathar_, Apr 01 2008