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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<n, b(n-1, k), [])[], seq(ilcm(c, n), c=b(n-1, k-1))])

    end:

T:= (n, 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-Fran├žois 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<n else [0]

    return w + [lcm(c, n) for c in b(n-1, k-1)]

def T(n, k): return add(b(n, k))

flatten([[T(n, k) for k in (0..n)] for n in (0..10)])

# Peter Luschny, Jul 29 2013

CROSSREFS

Row sums give A226037. Cf. A096179, A181854.

Sequence in context: A144250 A156367 A193593 * A008276 A094638 A196844

Adjacent sequences:  A181850 A181851 A181852 * A181854 A181855 A181856

KEYWORD

nonn,tabl

AUTHOR

Peter Luschny, Dec 06 2010

STATUS

approved

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Last modified October 18 07:58 EDT 2018. Contains 316307 sequences. (Running on oeis4.)