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A268482
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Triangle that arise in the study of Galois polynomials.
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0
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1, -1, 8, 4, -76, 264, -33, 1248, -9735, 22080, 456, -32088, 440448, -2085096, 3715440, -9460, 1216600, -26297700, 205444800, -704121000, 1087450320, 274800, -64995600, 2073673920, -23974142160, 129203087760, -354403429920, 500558083200
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table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,3
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LINKS
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EXAMPLE
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First few rows are:
1;
-1, 8;
4, -76, 264;
-33, 1248, -9735, 22080;
456, -32088, 440448, -2085096, 3715440;
...
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MATHEMATICA
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c[k_] := c[k] = 1 - Sum[Binomial[k, j] Binomial[k-1, j-1] c[j], {j, k-1}];
eul[n_, x_] := Sum[(-1)^j Binomial[n+1, j] (x-j+1)^n, {j, 0, x+1}];
G[k_, m_] := G[k, m] = If [k==0 && m==0, 1, Sum[Binomial[k, j] Binomial[ k-1, j-1] c[j] Sum[eul[2j-1, i-1] G[k-j, m-i], {i, m}]/(2j-1)!, {j, k}]];
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PROG
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(PARI) C(k) = {my(j); 1 - sum(j=1, k-1, binomial(k, j)*binomial(k-1, j-1)*C(j))};
eul(n, x) = {my(j); sum(j=0, x+1, (-1)^j*binomial(n+1, j)*(x+1-j)^n)};
G(k, m) = if ((k==0) && (m==0), 1, sum(j=1, k, binomial(k, j)*binomial(k-1, j-1)*C(j)*sum(i=1, m, eul(2*j-1, i-1)*G(k-j, m-i))/(2*j-1)!));
tabl(nn) = for (n=1, nn, for (k=1, n, print1((2*n-1)!*G(n, k), ", ")); print(); );
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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