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A125553
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Triangle read by rows: T(n,k) = S1(n,k)*2^k, where S1(n,k) is an unsigned Stirling number of the first kind (cf. A008275) (n >= 1, 1 <= k <= n).
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1
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2, 2, 4, 4, 12, 8, 12, 44, 48, 16, 48, 200, 280, 160, 32, 240, 1096, 1800, 1360, 480, 64, 1440, 7056, 12992, 11760, 5600, 1344, 128, 10080, 52272, 105056, 108304, 62720, 20608, 3584, 256, 80640, 438336, 944992, 1076544, 718368, 290304, 69888, 9216
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Row sums are factorial numbers.
Subtriangle (for 1<=k<=n) of triangle given by [0,1,1,2,2,3,3,4,4,5,5,...] DELTA [2,0,2,0,2,0,2,0,2,0,...] where DELTA is the operator defined in A084938. - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jan 05 2007
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FORMULA
| E.g.f.: 1/(1-x)^(2y) - Geoffrey Critzer, Dec 14 2011
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EXAMPLE
| Triangle begins:
2
2 4
4 12 8
12 44 48 16
48 200 280 160 32
Triangle [0,1,1,2,2,3,3,...] DELTA [2,0,2,0,2,0,2,...], for 0<=k<=n, begins:
1;
0, 2;
0, 2, 4;
0, 4, 12, 8;
0, 12, 44, 48, 16;
0, 48, 200, 280, 160, 32;
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MAPLE
| with(combinat): T:=(n, k)->2^k*abs(stirling1(n, k)): for n from 1 to 10 do seq(T(n, k), k=1..n) od; # yields sequence in triangular form - Emeric Deutsch (deutsch(AT)duke.poly.edu), Jan 05 2007
A008275 := proc(n, k) if n = 0 and k = 0 then 1 ; elif n = 0 or k = 0 then 0 ; else A008275(n-1, k-1)-(n-1)*A008275(n-1, k) ; fi ; end ; A125553 := proc(n, k) abs(A008275(n, k)*2^k) ; end ; nmax := 10 ; for n from 1 to nmax do for k from 1 to n do printf("%d, ", A125553(n, k)) ; od ; od ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jan 12 2007
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MATHEMATICA
| Flatten[Table[Table[2^k Abs[StirlingS1[n, k]], {k, 1, n}], {n, 1, 8}]] (* Geoffrey Critzer, Dec 14 2011 *)
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CROSSREFS
| Cf. A008275.
Sequence in context: A005293 A057784 A081164 * A138317 A103659 A069947
Adjacent sequences: A125550 A125551 A125552 * A125554 A125555 A125556
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KEYWORD
| nonn,tabl,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Jan 04 2007
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EXTENSIONS
| More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jan 12 2007
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