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(MAGMA) /* As triangle */ [[5^(n-k)*Binomial(n-1, k-1)*Factorial(n) / Factorial(k): k in [1..n]]: n in [1.. 15]]; // Vincenzo Librandi, Jul 27 2019
easy,nonn,tabl,easy,changed
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(MAGMA) /* As triangle */ [[5^(n-k)*Binomial(n-1, k-1)*Factorial(n) / Factorial(k): k in [1..n]]: n in [1.. 15]]; // Vincenzo Librandi, Jul 27 2019
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Table[5^(n - k) * Binomial[n - 1, k - 1] * n! / k!, {n, 1, 10}, {k, 1, n}] // Flatten (* Amiram Eldar, Jul 13 2019 *)
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The fifth power of the unsigned Lah triangular matrix A105278.
1, 10, 1, 150, 30, 1, 3000, 900, 60, 1, 75000, 30000, 3000, 100, 1, 2250000, 1125000, 150000, 7500, 150, 1, 78750000, 47250000, 7875000, 525000, 15750, 210, 1, 3150000000, 2205000000, 441000000, 36750000, 1470000, 29400, 280, 1, 141750000000, 113400000000, 26460000000, 2646000000, 132300000, 3528000, 50400, 360, 1, 7087500000000, 6378750000000, 1701000000000, 198450000000, 11907000000, 396900000, 7560000, 81000, 450, 1
Cf. A105278.
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