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 A137268 Triangle T(n, k) = k! * (k+1)^(n-k), read by rows. 3
 1, 2, 2, 4, 6, 6, 8, 18, 24, 24, 16, 54, 96, 120, 120, 32, 162, 384, 600, 720, 720, 64, 486, 1536, 3000, 4320, 5040, 5040, 128, 1458, 6144, 15000, 25920, 35280, 40320, 40320, 256, 4374, 24576, 75000, 155520, 246960, 322560, 362880, 362880 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Essentially the same as A104001. LINKS G. C. Greubel, Rows n = 1..50 of the triangle, flattened Fan Chung and R. L. Graham, Primitive juggling sequences, Am. Math. Monthly 115 (3) (2008) 185-194. FORMULA J(b, n) = (b+1)^(n-b)*b! if n > b, otherwise n! (notation of Chung and Graham). From G. C. Greubel, Nov 28 2022: (Start) T(n, k) = k! * (k+1)^(n-k). T(n, n-2) = 2*A074143(n), n > 1. T(2*n, n) = A152684(n). T(2*n, n-1) = A061711(n). T(2*n+1, n+1) = A066319(n). (End) EXAMPLE Triangle begins as: 1; 2, 2; 4, 6, 6; 8, 18, 24, 24; 16, 54, 96, 120, 120; 32, 162, 384, 600, 720, 720; 64, 486, 1536, 3000, 4320, 5040, 5040; 128, 1458, 6144, 15000, 25920, 35280, 40320, 40320; 256, 4374, 24576, 75000, 155520, 246960, 322560, 362880, 362880; 512, 13122, 98304, 375000, 933120, 1728720, 2580480, 3265920, 3628800, 3628800; MATHEMATICA T[n_, k_]:= k!*(k+1)^(n-k); Table[T[n, k], {n, 12}, {k, n}]//Flatten PROG (Magma) [Factorial(k)*(k+1)^(n-k): k in [1..n], n in [1..12]]; // G. C. Greubel, Nov 28 2022 (SageMath) def A137268(n, k): return factorial(k)*(k+1)^(n-k) flatten([[A137268(n, k) for k in range(1, n+1)] for n in range(14)]) # G. C. Greubel, Nov 28 2022 CROSSREFS Cf. A061711, A066319, A074143, A104001, A152684. Sequence in context: A309075 A039731 A005341 * A008130 A055388 A065457 Adjacent sequences: A137265 A137266 A137267 * A137269 A137270 A137271 KEYWORD nonn,tabl,easy AUTHOR Roger L. Bagula, Mar 12 2008 EXTENSIONS Edited by G. C. Greubel, Nov 28 2022 STATUS approved

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Last modified May 27 02:41 EDT 2024. Contains 372847 sequences. (Running on oeis4.)