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 A174298 Triangle T(n, k) = binomial(n, k)*( n!/k! if floor(n/2) >= k otherwise n!/(n-k)! ), read by rows. 1
 1, 1, 1, 2, 4, 2, 6, 18, 18, 6, 24, 96, 72, 96, 24, 120, 600, 600, 600, 600, 120, 720, 4320, 5400, 2400, 5400, 4320, 720, 5040, 35280, 52920, 29400, 29400, 52920, 35280, 5040, 40320, 322560, 564480, 376320, 117600, 376320, 564480, 322560, 40320, 362880, 3265920, 6531840, 5080320, 1905120, 1905120, 5080320, 6531840, 3265920, 362880 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS G. C. Greubel, Rows n = 0..50 of the triangle, flattened FORMULA T(n, k) = binomial(n, k)*( n!/k! if floor(n/2) >= k otherwise n!/(n-k)! ). From G. C. Greubel, Nov 24 2021: (Start) T(n, k) = binomial(n, k)^2*( (n-k)! if floor(n/2) >= k otherwise k! ). T(n, 0) = T(n, n) = n!. T(n, k) = T(n, n-k). T(2*n, n) = (-1)^n*A295383(n). (End) EXAMPLE Triangle begins as: 1; 1, 1; 2, 4, 2; 6, 18, 18, 6; 24, 96, 72, 96, 24; 120, 600, 600, 600, 600, 120; 720, 4320, 5400, 2400, 5400, 4320, 720; 5040, 35280, 52920, 29400, 29400, 52920, 35280, 5040; 40320, 322560, 564480, 376320, 117600, 376320, 564480, 322560, 40320; MATHEMATICA T[n_, k_]:= Binomial[n, k]*If[Floor[n/2]>=k, n!/k!, n!/(n-k)!]; Table[T[n, k], {n, 0, 12}, {k, 0, n}]//Flatten PROG (Magma) A174298:= func< n, k | Floor(n/2) gt k select Factorial(n-k)*Binomial(n, k)^2 else Factorial(k)*Binomial(n, k)^2 >; [A174298(n, k): k in [0..n], n in [0..12]]; // G. C. Greubel, Nov 24 2021 (Sage) def A174298(n, k): return binomial(n, k)^2*( factorial(n-k) if ((n//2) > k-1) else factorial(k)) flatten([[A174298(n, k) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Nov 24 2021 CROSSREFS Cf. A295383. Sequence in context: A138024 A167656 A253666 * A196347 A021012 A229460 Adjacent sequences: A174295 A174296 A174297 * A174299 A174300 A174301 KEYWORD nonn,tabl AUTHOR Roger L. Bagula, Mar 15 2010 EXTENSIONS Edited by G. C. Greubel, Nov 24 2021 STATUS approved

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Last modified May 20 14:08 EDT 2024. Contains 372717 sequences. (Running on oeis4.)