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 A181853 Triangle read by rows: T(n,k) = Sum_{c in C(n,k)} lcm(c) where C(n,k) is the set of all k-subsets of {1,2,...,n}. 5
 1, 1, 1, 1, 3, 2, 1, 6, 11, 6, 1, 10, 31, 34, 12, 1, 15, 81, 189, 182, 60, 1, 21, 141, 393, 494, 282, 60, 1, 28, 288, 1380, 3245, 3740, 2034, 420, 1, 36, 456, 2716, 8293, 13268, 11338, 4908, 840, 1, 45, 726, 5578, 22207, 47351, 57598, 40602, 15564, 2520 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS The C(n,k) are also called combinations of n with size k (see A181842). Main diagonal gives: A003418. Lower diagonal gives: A094308. Column k=1 gives: A000217. - Alois P. Heinz, Jul 29 2013 LINKS Alois P. Heinz, Rows n = 0..46, flattened EXAMPLE [0] 1 [1] 1 1 [2] 1 3 2 [3] 1 6 11 6 [4] 1 10 31 34 12 [5] 1 15 81 189 182 60 [6] 1 21 141 393 494 282 60 MAPLE with(combstruct): a181853_row := proc(n) local k, L, l, R, comb; R := NULL; for k from 0 to n do L := 0; comb := iterstructs(Combination(n), size=k): while not finished(comb) do l := nextstruct(comb); L := L + ilcm(op(l)); od; R := R, L; od; R end: # second Maple program: b:= proc(n, k) option remember; `if`(k=0, [1], [`if`(k add(c, c=b(n, k)): seq(seq(T(n, k), k=0..n), n=0..10); # Alois P. Heinz, Jul 29 2013 # third Maple program: b:= proc(n, m) option remember; expand(`if`(n=0, m, b(n-1, ilcm(m, n))*x+b(n-1, m))) end: T:= n-> (p-> seq(coeff(p, x, i), i=0..n))(b(n, 1)): seq(T(n), n=0..10); # Alois P. Heinz, Sep 05 2023 MATHEMATICA t[_, 0] = 1; t[n_, k_] := Sum[LCM @@ c, {c, Subsets[Range[n], {k}]}]; Table[t[n, k], {n, 0, 8}, {k, 0, n}] // Flatten (* Jean-François Alcover, Jul 29 2013 *) PROG (Sage) # (After Alois P. Heinz) @CachedFunction def b(n, k): if k == 0: return [1] w = b(n-1, k) if k

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Last modified April 22 01:34 EDT 2024. Contains 371887 sequences. (Running on oeis4.)