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A094304 Sum of all possible sums formed from all but one of the previous terms, starting 1. 3
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; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Apart from initial 1, same sequence as A001563. Additive analog 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. - Jaroslav Krizek, Oct 16 2009

LINKS

Table of n, a(n) for n=1..23.

Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets

FORMULA

a(n) = (n-2)!(n-2) for n>=2. - Emeric Deutsch, May 01 2008

G.f.: x*T(0), where T(k) = 1 - x^2*(k+1)^2/(x^2*(k+1)^2 - (1 -x -2*x*k)*(1 -3*x -2*x*k)/T(k+1) ); (continued fraction). - Sergei N. Gladkovskii, Nov 10 2013

a(n) = S1(n,1) - S1(n-1,1), where S1 are the unsigned Stirling cycle numbers. - Peter Luschny, Apr 10 2016

a(n) = A122974(n-1,n-1). - Alois P. Heinz, Nov 24 2019

EXAMPLE

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.

a(5) = (a(1)+a(2)+a(3)) +(a(1)+a(2)+ a(4)) +(a(1)+a(3)+a(4)) +(a(2)+a(3)+a(4)) = (1+0+1) +(1+0+4) +(1+1+4) +(0+1+4) = 2 + 5 + 6 + 5 = 18.

MAPLE

a := n -> (n-2)*(n-2)!: 1, seq(a(n), n=2..23); # Emeric Deutsch, May 01 2008

MATHEMATICA

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 *)

PROG

(PARI) v=vector(30); v[1]=1; v[2]=0; for(n=3, #v, s=0; for(i=1, 2^(n-1)-1, vb=binary(i); if(hammingweight(vb)==n-2, s=s+sum(j=1, #vb, if(vb[j], v[n-#vb+j-1])))); v[n]=s; print1(s, ", ")) /* Ralf Stephan, Sep 22 2013 */

CROSSREFS

Cf. A001563, A057438, A122974.

Sequence in context: A180567 A152392 A001563 * A094258 A234854 A334735

Adjacent sequences:  A094301 A094302 A094303 * A094305 A094306 A094307

KEYWORD

nonn

AUTHOR

Amarnath Murthy, Apr 29 2004

EXTENSIONS

Edited by N. J. A. Sloane, May 29 2006

STATUS

approved

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Last modified August 17 00:01 EDT 2022. Contains 356180 sequences. (Running on oeis4.)