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 A003992 Square array read by upwards antidiagonals: T(n,k) = n^k for n >= 0, k >= 0. 19
 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; text; internal format)
 OFFSET 0,8 COMMENTS If the array is transposed, T(n,k) is the number of oriented rows of n colors using up to k different colors. The formula would be T(n,k) = [n==0] + [n>0]*k^n. The generating function for column k would be 1/(1-k*x). For T(3,2)=8, the rows are AAA, AAB, ABA, ABB, BAA, BAB, BBA, and BBB. - Robert A. Russell, Nov 08 2018 T(n,k) is the number of multichains of length n from {} to [k] in the Boolean lattice B_k. - Geoffrey Critzer, Apr 03 2020 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, Oct 22 2004 E.g.f.: Sum T(n,k)*x^n/n!*y^k/k! = e^(x*e^y). - Franklin T. Adams-Watters, 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 Table[If[k == 0, 1, (n - k)^k], {n, 0, 11}, {k, 0, n}]//Flatten PROG (PARI) T(n, k) = (n-k)^k \\ Charles R Greathouse IV, Feb 07 2017 (MAGMA) [[(n-k)^k: k in [0..n]]: n in [0..10]]; // G. C. Greubel, Nov 08 2018 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. Cf. A277504 (unoriented), A293500 (chiral). Sequence in context: A213276 A210391 A071921 * A246118 A171882 A214075 Adjacent sequences:  A003989 A003990 A003991 * A003993 A003994 A003995 KEYWORD easy,nice,nonn,tabl AUTHOR EXTENSIONS More terms from David W. Wilson Edited by Paul D. Hanna, Oct 22 2004 STATUS approved

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Last modified December 1 21:02 EST 2020. Contains 338858 sequences. (Running on oeis4.)