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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..25, 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 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 January 17 06:55 EST 2019. Contains 319207 sequences. (Running on oeis4.)