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A226037 a(n) = Sum_{c in P(n)} lcm(c) where P(n) is the set of all subsets of {1,2,...,n}. 2
1, 2, 6, 24, 88, 528, 1392, 11136, 41856, 192192, 516032, 6192384, 13270272, 185783808, 511526400, 1163742720, 4403449344, 79262088192, 199280729088, 3985614581760, 8463108648960, 19276630732800, 54618972549120, 1310855341178880, 2751134770298880, 17228042511482880 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..32

FORMULA

a(n) = Sum_{k=0..n} Sum_{c in binomial(n,k)} lcm(c) where C(n,k) are the combinations of n with size k.

EXAMPLE

a(4) = lcm{} + lcm{1} + lcm{2} + lcm{3} + lcm{4} + lcm{1,2} + lcm{1,3} + lcm{1,4} + lcm{2,3} + lcm{2,4} + lcm{3,4} + lcm{1,2,3} + lcm{1,2,4} + lcm{1,3,4} + lcm{2,3,4} + lcm{1,2,3,4}

= 1 + 1 + 2 + 3 + 4 + 2 + 3 + 4 + 6 + 4 + 12 + 6 + 4 + 12 + 12 + 12 = 88.

MAPLE

with(combstruct):

A226037 := proc(n) local R, c; R := 0; c := iterstructs(Combination(n)):

while not finished(c) do R := R + ilcm(op(nextstruct(c))) od; R end: seq(A226037(n), n=0..25);

MATHEMATICA

a[n_] := Total[LCM @@@ Rest[Subsets[Range[n]]]] + 1; Table[Print[an = a[n]]; an, {n, 0, 25}] (* Jean-Fran├žois Alcover, Jan 15 2014 *)

PROG

(Sage) # (After Alois P. Heinz)

@CachedFunction

def C(n, k):

    if k == 0: return [1]

    w = C(n-1, k) if k < n else [0]

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

def A226037(n): return add(add(C(n, k)) for k in (0..n))

[A226037(n) for n in (0..20)]

CROSSREFS

Row sums of triangle A181853.

Sequence in context: A003759 A217527 A293774 * A003450 A192466 A115220

Adjacent sequences:  A226034 A226035 A226036 * A226038 A226039 A226040

KEYWORD

nonn

AUTHOR

Peter Luschny, Jul 30 2013

STATUS

approved

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Last modified April 24 00:02 EDT 2019. Contains 322404 sequences. (Running on oeis4.)