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 A062275 Array A(n, k) = n^k * k^n, n, k >= 0, read by antidiagonals. 4
 1, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 3, 16, 3, 0, 0, 4, 72, 72, 4, 0, 0, 5, 256, 729, 256, 5, 0, 0, 6, 800, 5184, 5184, 800, 6, 0, 0, 7, 2304, 30375, 65536, 30375, 2304, 7, 0, 0, 8, 6272, 157464, 640000, 640000, 157464, 6272, 8, 0, 0, 9, 16384, 750141, 5308416, 9765625 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,8 COMMENTS Here 0^0 is defined to be 1. - Wolfdieter Lang, May 27 2018 LINKS Eric Chen, Table of n, a(n) for n = 0..5049 (first 100 antidiagonals) FORMULA From Wolfdieter Lang, May 22 2018: (Start) As a sequence: a(n) = A003992(n)*A004248(n). As a triangle: T(n, k) = (n-k)^k * k^(n-k), for n >= 1 and k = 1..n. (End) EXAMPLE A(3, 2) = 3^2 * 2^3 = 9*8 = 72. The array A(n, k) begins: n\k 0 1 2 3 4 5 6 7 8 9 10 ... 0: 1 0 0 0 0 0 0 0 0 0 0 ... 1: 0 1 2 3 4 5 6 7 8 9 10 ... 2: 0 2 16 72 256 800 2304 6272 16384 41472 102400 ... 3: 0 3 72 729 5184 30375 157464 750141 3359232 14348907 59049000 ... ... The triangle T(n, k) begins: n\k 0 1 2 3 4 5 6 7 8 9 ... 0: 1 1: 0 0 2: 0 1 0 3: 0 2 2 0 4: 0 3 16 3 0 5: 0 4 72 72 4 0 6: 0 5 256 729 256 5 0 7: 0 6 800 5184 5184 800 6 0 8: 0 7 2304 30375 65536 30375 2304 7 0 9: 0 8 6272 157464 640000 640000 157464 6272 8 0 ... - Wolfdieter Lang, May 22 2018 MATHEMATICA {{1}}~Join~Table[(#^k k^#) &[n - k], {n, 10}, {k, 0, n}] // Flatten (* Michael De Vlieger, May 24 2018 *) PROG (PARI) t1(n)=n-binomial(round(sqrt(2+2*n)), 2) t2(n)=binomial(floor(3/2+sqrt(2+2*n)), 2)-(n+1) a(n)=t1(n)^t2(n)*t2(n)^t1(n) \\ Eric Chen, Jun 09 2018 CROSSREFS Columns and rows of A, or columns and diagonals of T, include A000007, A001477, A007758, A062074, A062075 etc. Diagonals of A include A062206, A051443, A051490. Sum of rows of T are A062817(n), for n >= 1 Cf. A055651, A055652, A303990. Sequence in context: A329331 A355664 A254040 * A138270 A317643 A179011 Adjacent sequences: A062272 A062273 A062274 * A062276 A062277 A062278 KEYWORD nonn,tabl,easy AUTHOR Henry Bottomley, Jul 02 2001 STATUS approved

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Last modified September 28 01:19 EDT 2023. Contains 365714 sequences. (Running on oeis4.)