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%I #6 Feb 28 2020 22:24:29
%S 30,135,490,2436,1575,10143,4565,37338,1300156,792,12310,124754,1575,
%T 31185,386155,26543660,75175,1121505,4835271870,5604,173525,3087735,
%U 10143,386155,8118264,1327710076,4328363658647,25025873760111
%N Irregular triangle which contains in row n those partition numbers A000041(n*(2m+1) + m + 2) which are congruent to 0 mod (2m+1) for 1 <= m <= n.
%D Robert Kanigel, The Man Who Knew Infinity, Washington Square Press, New York, 1991, page 302.
%e The first line contains A000041(9)=30 from n=2 and m=1 and A000041(14)=135 from n=2 and m=2.
%e The fifth line contains A000041(29)=4565 from n=5 and m=2, A000041(40)=37338 from n=5 and m=3, and A000041(62)=1300156 from n=m=5.
%e The array starts
%e 30, 135;
%e 490, 2436;
%e 1575, 10143;
%e 4565, 37338, 1300156;
%e 792, 12310, 124754;
%e 1575, 31185, 386155, 26543660;
%e 75175, 1121505, 4835271870;
%e 5604, 173525, 3087735;
%e 10143, 386155, 8118264, 1327710076, 4328363658647, 25025873760111;
%t b = Table[Flatten[Table[If[Mod[a[[( 2*n + 1)*m + n + 2]], 2*n + 1] == 0, PartitionsP[(2*n + 1)*m + n + 2], {}], {n, 1, m}]], {m, 1, 10}] Flatten[b]
%Y Cf. A000041, A117749.
%K nonn,tabf
%O 2,1
%A _Roger L. Bagula_, Apr 14 2006
%E Comments and definition rephrased, offset corrected - the Assoc. Eds. of the OEIS, Jun 27 2010
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