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 A173476 Triangle T(n, k) = 1 + (k!)^2 - 2*k!*(n-k)! + ((n-k)!)^2, read by rows. 1
 1, 1, 1, 2, 1, 2, 26, 2, 2, 26, 530, 26, 1, 26, 530, 14162, 530, 17, 17, 530, 14162, 516962, 14162, 485, 1, 485, 14162, 516962, 25391522, 516962, 13925, 325, 325, 13925, 516962, 25391522, 1625621762, 25391522, 515525, 12997, 1, 12997, 515525, 25391522, 1625621762 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS G. C. Greubel, Rows n = 0..100 of the triangle, flattened FORMULA T(n, k) = 1 + ( (n-k)! - k! )^2. Sum_{k=0..n} T(n, k) = 1 + n + 2*A061062(n) - 2*A003149(n). - G. C. Greubel, Feb 19 2021 EXAMPLE Triangle begins as: 1; 1, 1; 2, 1, 2; 26, 2, 2, 26; 530, 26, 1, 26, 530; 14162, 530, 17, 17, 530, 14162; 516962, 14162, 485, 1, 485, 14162, 516962; 25391522, 516962, 13925, 325, 325, 13925, 516962, 25391522; 1625621762, 25391522, 515525, 12997, 1, 12997, 515525, 25391522, 1625621762; MATHEMATICA Table[((n-k)! -k!)^2 +1, {n, 0, 12}, {k, 0, n}]//Flatten (* modified by G. C. Greubel, Feb 19 2021 *) PROG (Sage) flatten([[(factorial(n-k) -factorial(k))^2 +1 for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Feb 19 2021 (Magma) [(Factorial(n-k) -Factorial(k))^2 +1: k in [0..n], n in [0..12]]; // G. C. Greubel, Feb 19 2021 CROSSREFS Cf. A003149, A061062. Sequence in context: A051502 A228690 A121721 * A281129 A136156 A191657 Adjacent sequences: A173473 A173474 A173475 * A173477 A173478 A173479 KEYWORD nonn,tabl AUTHOR Roger L. Bagula, Feb 19 2010 EXTENSIONS Edited by G. C. Greubel, Feb 19 2021 STATUS approved

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Last modified September 21 18:57 EDT 2023. Contains 365503 sequences. (Running on oeis4.)