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A046817
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Triangle of generalized Stirling numbers of 2nd kind.
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3
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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; internal format)
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OFFSET
| 0,3
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REFERENCES
| R. Fray, A generating function associated with the generalized Stirling numbers, Fib. Quart. 5 (1967), 356-366.
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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 (vladeta(AT)eunet.rs), Dec 14 2003
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EXAMPLE
| Triangle begins
1;
1, 2;
1, 6, 5;
1, 12, 32, 15;
1, 20, 110, 175, 52;
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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]] (* From Jean-François Alcover, Apr 26 2011 *)
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CROSSREFS
| Diagonals give A000558, A000559, A000110, A002378, etc.
Cf. A039810.
Sequence in context: A145960 A205455 A108767 * A193817 A008970 A055896
Adjacent sequences: A046814 A046815 A046816 * A046818 A046819 A046820
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KEYWORD
| tabl,nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from David W. Wilson (davidwwilson(AT)comcast.net), Jan 13, 2000.
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