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Search: id:A094304
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| A094304 |
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a(1) = 1; for n > 1, a(n) = sum of all possible sums of n-2 previous terms. |
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+0
2
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| 1, 0, 1, 4, 18, 96, 600, 4320, 35280, 322560, 3265920, 36288000, 439084800, 5748019200, 80951270400, 1220496076800, 19615115520000, 334764638208000, 6046686277632000, 115242726703104000, 2311256907767808000, 48658040163532800000, 1072909785605898240000
(list; graph; listen)
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OFFSET
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1,4
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COMMENT
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Apart from initial 1, same sequence as A001563. Additive analogue of A057438.
a(1) = 1, for n >= 2: a(n) = sum of previous terms * (n-2) = (Sum_(i=1...n-2) a(i)) * (n-2). a(n) = A001563(n-2) = A094258(n-1) for n >= 3. [From Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Oct 16 2009]
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LINKS
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Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets
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FORMULA
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a(n)=(n-2)!(n-2) for n>=2. - Emeric Deutsch (deutsch(AT)duke.poly.edu), May 01 2008
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EXAMPLE
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a(2) = 0 as there is only one previous term and empty sum is taken to be 0.
a(4) = (a(1) +a(2))+ (a(1) +a(3)) + (a(2) +a(3)) = (1+0) +(1+1) +(0+1) = 4.
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MAPLE
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a:=proc(n) options operator, arrow: factorial(n-2)*(n-2) end proc:1, seq(a(n), n=2..23); - Emeric Deutsch (deutsch(AT)duke.poly.edu), May 01 2008
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MATHEMATICA
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In[2]:= l = {1}; Do[k = Length[l] - 1; p = Plus @@ Flatten[Select[Subsets[l], Length[ # ]==k& ]]; AppendTo[l, p], {n, 20}]; l (Ryan Propper, May 28 2006)
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CROSSREFS
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Cf. A001563, A057438.
Sequence in context: A005777 A152392 A001563 this_sequence A094258 A086681 A054139
Adjacent sequences: A094301 A094302 A094303 this_sequence A094305 A094306 A094307
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KEYWORD
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nonn
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Apr 29 2004
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EXTENSIONS
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Edited by N. J. A. Sloane (njas(AT)research.att.com), May 29 2006
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