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%I #31 Sep 03 2019 09:18:51
%S 1,1,2,1,6,5,1,12,32,15,1,20,110,175,52,1,30,280,945,1012,203,1,42,
%T 595,3465,8092,6230,877,1,56,1120,10010,40992,70756,40819,4140,1,72,
%U 1932,24570,156072,479976,638423,283944,21147,1,90,3120,53550,487704,2350950,5660615,5971350
%N Triangle of generalized Stirling numbers of 2nd kind.
%H Tilman Piesk, <a href="/A046817/b046817.txt">First 100 rows, flattened</a>
%H R. Fray, <a href="http://www.fq.math.ca/Scanned/5-4/fray.pdf">A generating function associated with the generalized Stirling numbers</a>, Fib. Quart. 5 (1967), 356-366.
%F a(n, k) = Sum_{i=k..n} S2(n, i)*S2(i, k).
%F E.g.f.: exp(exp(exp(x*y)-1)-1)^(1/y). - _Vladeta Jovovic_, Dec 14 2003
%e Triangle begins:
%e k = 0 1 2 3 4 sum
%e n
%e 1 1 1
%e 2 1 2 3
%e 3 1 6 5 12
%e 4 1 12 32 15 60
%e 5 1 20 110 175 52 358
%t a[n_, k_] = Sum[StirlingS2[n, i]*StirlingS2[i, k], {i, k, n}]; Flatten[Table[a[n, k], {n, 1, 10}, {k, n, 1, -1}]][[1 ;; 53]] (* _Jean-François Alcover_, Apr 26 2011 *)
%Y Diagonals give A000558, A000559, A000110, A002378, etc.
%Y Row sums give A000258.
%Y Horizontal mirror triangle is A039810 (matrix square of Stirling2).
%K tabl,nonn,easy,nice
%O 0,3
%A _N. J. A. Sloane_
%E More terms from _David W. Wilson_, Jan 13 2000
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