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 A327027 T(n, k) = (1/n) * Sum_{d|n} phi(d) * A241171(n/d, k) for n >= 1, T(0, k) = 0^k. Triangle read by rows for 0 <= k <= n. 2
 1, 0, 1, 0, 1, 3, 0, 1, 10, 30, 0, 1, 33, 315, 630, 0, 1, 102, 2646, 15120, 22680, 0, 1, 348, 21135, 263340, 1039500, 1247400, 0, 1, 1170, 167310, 4118400, 32432400, 97297200, 97297200, 0, 1, 4113, 1333080, 61757010, 871620750, 4937832900, 11918907000, 10216206000 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 COMMENTS We assume A241171 extended to its (0, 0)-based form. LINKS Table of n, a(n) for n=0..44. EXAMPLE [0] 1; [1] 0, 1; [2] 0, 1, 3; [3] 0, 1, 10, 30; [4] 0, 1, 33, 315, 630; [5] 0, 1, 102, 2646, 15120, 22680; [6] 0, 1, 348, 21135, 263340, 1039500, 1247400; [7] 0, 1, 1170, 167310, 4118400, 32432400, 97297200, 97297200; MAPLE A327027 := (n, k)-> `if`(n=0, 1, (1/n)*add(phi(d)*A241171(n/d, k), d=divisors(n))): seq(seq(A327027(n, k), k=0..n), n=0..6); MATHEMATICA A327027[0, k_] := 1; A327027[n_, k_] := DivisorSum[n, EulerPhi[#] A241171[n/#, k] &] / n; Table[A327027[n, k], {n, 0, 8}, {k, 0, n}] // Flatten PROG (Sage) # uses[DivisorTriangle from A327029, A241171] DivisorTriangle(euler_phi, A241171, 8, lambda n: 1/n if n > 1 else 1) CROSSREFS Cf. A327021 (main diagonal), A327026 (row sums), A241171, A327029. Sequence in context: A307657 A269939 A239731 * A145881 A232223 A245111 Adjacent sequences: A327024 A327025 A327026 * A327028 A327029 A327030 KEYWORD nonn,tabl AUTHOR Peter Luschny, Aug 20 2019 STATUS approved

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Last modified August 6 22:48 EDT 2024. Contains 375002 sequences. (Running on oeis4.)