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A025135
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(n-1)st elementary symmetric function of binomial(n,0), binomial(n,1), ..., binomial(n,n).
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2
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1, 4, 22, 238, 5825, 345600, 51583084, 19765932032, 19661794008192, 51082239411000000, 347836712523276735000, 6221718604078720792473600, 292819054882445795002015111824, 36313083181879002042916296055971840, 11881691691176915544450299522846484375000
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OFFSET
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1,2
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COMMENTS
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The k-th elementary symmetric functions of the terms binomial(n,j), j=0..n, form a triangle T(n,k), 0 <= k <= n, n >= 0:
1
1 2
1 4 5
1 8 22 24
1 16 93 238 256
1 32 386 2180 5825 6500
1 64 1586 19184 117561 345600 407700
1 128 6476 164864 2229206 15585920 51583084 64538880
...
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LINKS
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MATHEMATICA
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a[n_] := SymmetricPolynomial[n-1, Table[Binomial[n, k], {k, 0, n}]]; a /@ Range[18] (* Jean-François Alcover, Jul 12 2011 *)
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PROG
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(PARI)
ESym(u)={my(v=vector(#u+1)); v[1]=1; for(i=1, #u, my(t=u[i]); forstep(j=i, 1, -1, v[j+1]+=v[j]*t)); v}
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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