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 A046817 Triangle of generalized Stirling numbers of 2nd kind. 4
 1, 1, 2, 1, 6, 5, 1, 12, 32, 15, 1, 20, 110, 175, 52, 1, 30, 280, 945, 1012, 203, 1, 42, 595, 3465, 8092, 6230, 877, 1, 56, 1120, 10010, 40992, 70756, 40819, 4140, 1, 72, 1932, 24570, 156072, 479976, 638423, 283944, 21147, 1, 90, 3120, 53550, 487704, 2350950, 5660615, 5971350 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Tilman Piesk, First 100 rows, flattened R. Fray, A generating function associated with the generalized Stirling numbers, Fib. Quart. 5 (1967), 356-366. FORMULA a(n, k) = Sum_{i=k..n} S2(n, i)*S2(i, k). E.g.f.: exp(exp(exp(x*y)-1)-1)^(1/y). - Vladeta Jovovic, Dec 14 2003 EXAMPLE Triangle begins: k = 0 1 2 3 4 sum n 1 1 1 2 1 2 3 3 1 6 5 12 4 1 12 32 15 60 5 1 20 110 175 52 358 MATHEMATICA 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 *) CROSSREFS Diagonals give A000558, A000559, A000110, A002378, etc. Row sums give A000258. Horizontal mirror triangle is A039810 (matrix square of Stirling2). Sequence in context: A350510 A259332 A108767 * A193817 A227159 A294439 Adjacent sequences: A046814 A046815 A046816 * A046818 A046819 A046820 KEYWORD tabl,nonn,easy,nice AUTHOR N. J. A. Sloane EXTENSIONS More terms from David W. Wilson, Jan 13 2000 STATUS approved

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Last modified August 14 22:58 EDT 2024. Contains 375167 sequences. (Running on oeis4.)