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A260613
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Triangle read by rows: T(n, k) = coefficient of x^(n-k) in Product_{m=1..n} (x+prime(m)); 0 <= k <= n, n >= 0.
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5
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1, 1, 2, 1, 5, 6, 1, 10, 31, 30, 1, 17, 101, 247, 210, 1, 28, 288, 1358, 2927, 2310, 1, 41, 652, 5102, 20581, 40361, 30030, 1, 58, 1349, 16186, 107315, 390238, 716167, 510510, 1, 77, 2451, 41817, 414849, 2429223, 8130689, 14117683, 9699690
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OFFSET
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0,3
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COMMENTS
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Up to signs and order of coefficients the same as A070918. Except for signs and the first column the same as A238146. - M. F. Hasler, Aug 13 2015
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LINKS
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FORMULA
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EXAMPLE
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The triangle starts:
Row 0: 1;
Row 1: 1, 2; Coefficients of x + 2.
Row 2: 1, 5, 6; Coefficients of (x+2)(x+3) = x^2 + 5x + 6.
Row 3: 1, 10, 31, 30; Coeff's of (x+2)(x+3)(x+5) = x^3 + 10x^2 + 31x + 30.
Row 5: 1, 17, 101, 247, 210;
Row 6: 1, 28, 288, 1358, 2927, 2310;
...
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MAPLE
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T:= n-> (p-> seq(coeff(p, x, n-i), i=0..n))(mul(x+ithprime(i), i=1..n)):
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MATHEMATICA
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row[n_] := CoefficientList[Product[x + Prime[m], {m, 1, n}] + O[x]^(n+1), x] // Reverse;
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PROG
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(PARI) tabl(nn) = {for (n=0, nn, polp = prod(k=1, n, x+prime(k)); forstep (k= n, 0, -1, print1(polcoeff(polp, k), ", "); ); print(); ); } \\ Michel Marcus, Aug 10 2015
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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