|
| |
|
|
A003992
|
|
Square array, read by antidiagonals, where T(n,k) = n^k for n>=0, k>=0.
|
|
9
| |
|
|
1, 1, 0, 1, 1, 0, 1, 2, 1, 0, 1, 3, 4, 1, 0, 1, 4, 9, 8, 1, 0, 1, 5, 16, 27, 16, 1, 0, 1, 6, 25, 64, 81, 32, 1, 0, 1, 7, 36, 125, 256, 243, 64, 1, 0, 1, 8, 49, 216, 625, 1024, 729, 128, 1, 0, 1, 9, 64, 343, 1296, 3125, 4096, 2187, 256, 1, 0, 1, 10, 81, 512, 2401, 7776, 15625, 16384, 6561, 512, 1, 0
(list; table; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,8
|
|
|
LINKS
| T. D. Noe, Rows n=0..50 of triangle, flattened
|
|
|
FORMULA
| E.g.f. Sum T(n,k)*x^n*y^k/k! = 1/(1-x*exp(y)). - Paul D. Hanna (pauldhanna(AT)juno.com), Oct 22 2004 E.g.f. Sum T(n,k)*x^n/n!*y^k/k! = e^(x*e^y). - Frank Adams (FrankTAW(AT)Netscape.net), Jun 23 2006
|
|
|
EXAMPLE
| Rows begin:
[1,0,0,0,0,0,0,0,...],
[1,1,1,1,1,1,1,1,...],
[1,2,4,8,16,32,64,128,...],
[1,3,9,27,81,243,729,2187,...],
[1,4,16,64,256,1024,4096,16384,...],
[1,5,25,125,625,3125,15625,78125,...],
[1,6,36,216,1296,7776,46656,279936,...],
[1,7,49,343,2401,16807,117649,823543,...],...
|
|
|
MATHEMATICA
| t[n_, k_] := n^k; t[0, 0] = 1; Table[ t[n - k, k], {n, 0, 11}, {k, 0, n}] // Flatten
|
|
|
CROSSREFS
| Rows 0-49 are A000007, A000012, A000079, A000244, A000302, A000351, A000400, A000420, A001018, A001019, A011557, A001020, A001021, A001022, A001023, A001024, A001025, A001026, A001027, A001029, A009964-A009992, A087752.
Columns 0-26 are A000012, A001477, A000290, A000578, A000583, A000584, A001014, A001015, A001016, A001017, A008454, A008455, A008456, A010801-A010813, A089081.
Main diagonal is A000312. Other diagonals include A000169, A007778, A000272, A008788. Antidiagonal sums are in A026898.
Cf. A099555.
Transpose is A004248. See A051128, A095884, A009999 for other versions.
Sequence in context: A071569 A118340 A071921 * A171882 A118345 A118350
Adjacent sequences: A003989 A003990 A003991 * A003993 A003994 A003995
|
|
|
KEYWORD
| easy,nice,nonn,tabl
|
|
|
AUTHOR
| Marc LeBrun (mlb(AT)well.com)
|
|
|
EXTENSIONS
| More terms from David W. Wilson (davidwwilson(AT)comcast.net)
Edited by Paul D. Hanna (pauldhanna(AT)juno.com), Oct 22 2004
|
| |
|
|
