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 A111823 Matrix log of triangle A111820, which shifts columns left and up under matrix 5th power; these terms are the result of multiplying each element in row n and column k by (n-k)!. 8
 0, 1, 0, -3, 5, 0, 16, -15, 25, 0, 2814, 80, -75, 125, 0, -1092180, 14070, 400, -375, 625, 0, -3603928080, -5460900, 70350, 2000, -1875, 3125, 0, 58978973128440, -18019640400, -27304500, 351750, 10000, -9375, 15625, 0, 5974833380453777520 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Column k equals 5^k multiplied by column 0 (A111824) when ignoring zeros above the diagonal. LINKS Table of n, a(n) for n=0..36. FORMULA T(n, k) = 5^k*T(n-k, 0) = A111824(n-k) for n>=k>=0. EXAMPLE Matrix log of A111820, with factorial denominators, begins: 0; 1/1!, 0; -3/2!, 5/1!, 0; 16/3!, -15/2!, 25/1!, 0; 2814/4!, 80/3!, -75/2!, 125/1!, 0; -1092180/5!, 14070/4!, 400/3!, -375/2!, 625/1!, 0; ... PROG (PARI) T(n, k, q=5)=local(A=Mat(1), B); if(n

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Last modified June 14 05:27 EDT 2024. Contains 373393 sequences. (Running on oeis4.)