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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-Fran├žois Alcover, Apr 26 2011 *)

CROSSREFS

Diagonals give A000558, A000559, A000110, A002378, etc.

Horizontal mirror triangle is A039810 (matrix square of Stirling2).

Sequence in context: A205455 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 January 17 18:48 EST 2019. Contains 319251 sequences. (Running on oeis4.)