A227866 Derived from von Mangoldt matrix sequence.
1, 1, 4, 27, 64, 3125, 288, 823543, 147456, 4251528, 460800, 285311670611, 111974400, 302875106592253, 3251404800, 13436928000, 106542032486400, 827240261886336764177, 1053455155200000, 1978419655660313589123979, 102395841085440000
Offset: 0
Keywords
Programs
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Mathematica
Clear[nn, t, n, k, i, s]; nn = 20; t[n_, 1] = 1; t[1, k_] = 1; t[n_, k_] := t[n, k] = If[n >= k, -Sum[t[n - i, k], {i, 1, k - 1}], -Sum[t[k - i, n], {i, 1, n - 1}]]; Exp[Table[Limit[Zeta[s]*Sum[If[n == 1, 0, t[n, k]]/k^(s - 1), {k, 1, n}], s -> 1], {n, 0, nn}]]*(Range[nn + 1] - 1)!
Formula
a(prime(n)) = A000312(prime(n)).
Comments