A074046
a(n)=a(n-1)*a(n-2)*a(n-3)*(1/a(n-1)+1/a(n-2)+1/a(n-3)) starting with a(1)=a(2)=1 and a(3)=2.
Original entry on oeis.org
1, 1, 2, 5, 17, 129, 2923, 428951, 1309535519, 565555596556379, 740857737860237412264699, 418997210078479016314891376985981834403, 310417325465458849274468827944195726858840449351291150876911355
Offset: 1
a(6)=17*5*2*(1/17+1/5+1/2)=129.
A094304
Sum of all possible sums formed from all but one of the previous terms, starting 1.
Original entry on oeis.org
1, 0, 1, 4, 18, 96, 600, 4320, 35280, 322560, 3265920, 36288000, 439084800, 5748019200, 80951270400, 1220496076800, 19615115520000, 334764638208000, 6046686277632000, 115242726703104000, 2311256907767808000, 48658040163532800000, 1072909785605898240000
Offset: 1
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.
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a := n -> (n-2)*(n-2)!: 1,seq(a(n), n=2..23); # Emeric Deutsch, May 01 2008
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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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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 */
A074056
a(n)=a(n-1)^3/a(n-2)^2+a(n-1)*a(n-2) with a(1)=a(2)=1.
Original entry on oeis.org
1, 1, 2, 10, 270, 199530, 109021396230, 32547610062433062370530, 2900907183084129462928443491816490142071240030, 23044287863704114233982017840826804806870854633710605340763217534502946372713488874512819930
Offset: 1
a(5)=10^3/2^2+10*2=250+20=270.
A108176
a(1) = 1, a(n) = (Sum_{k=1..floor(n/2)} 1/a(n + 1 - 2k))*(Product_{k=1..floor(n/2)} a(n + 1 - 2k)).
Original entry on oeis.org
1, 1, 1, 2, 3, 7, 23, 164, 3786, 620973, 2351006074, 1459911295051236, 3432260322166663402961472, 5010795611887306064313121202903094714708, 17198354961167628388233455836547370709483687001035342768448084064
Offset: 1
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a[1]:=1: for n from 2 to 25 do a[n]:=sum(1/a[n+1-2*j],j=1..floor(n/2))*product(a[n+1-2*k],k=1..floor(n/2)) od: seq(a[n],n=1..16); # Emeric Deutsch, Jun 14 2005
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a[1] = 1; a[n_] := a[n] = Sum[1/a[n + 1 - 2k], {k, Floor[n/2]}] Product[ a[n + 1 - 2k], {k, Floor[n/2]}]; Table[ a[n], {n, 15}] (* Robert G. Wilson v, Jun 14 2005 *)
A203903
a(n)=f(a(1),a(2),...,a(n-1)), where f=(n-2)-nd elementary symmetric function and a(1)=1, a(2)=1, a(3)=1.
Original entry on oeis.org
1, 1, 1, 3, 10, 103, 10639, 113191411, 12812295557045431, 164154917441086094769014370809371, 26946836920089791747880319422619013022132207748812110372395151551
Offset: 1
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a[1] = 1; a[2] = 1; a[3] = 1;
t[3] = {a[1], a[2], a[3]};
a[n_] := SymmetricPolynomial[n - 2, t[n - 1]]
t[n_] := Append[t[n - 1], {a[n]}]
Flatten[Table[a[n], {n, 1, 12}]] (* A203903 *)
Showing 1-5 of 5 results.
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