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A118687 A triangular array made from polynomial coefficients of A049614. 2
1, 1, -1, 1, -2, 1, 1, -3, 3, -1, 1, -4, 6, -4, 1, 1, -8, 22, -28, 17, -4, 1, -12, 54, -116, 129, -72, 16, 1, -36, 342, -1412, 2913, -3168, 1744, -384, 1, -60, 1206, -9620, 36801, -73080, 77776, -42240, 9216, 1, -252, 12726, -241172, 1883841, -7138872, 14109136, -14975232, 8119296, -1769472 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Same as an alternating sign Pascal's triangle up to row n=4.

LINKS

G. C. Greubel, Rows n = 0..50 of the triangle, flattened

FORMULA

T(n, k) = coefficients of Product_{k=0..n} (1 - A049614(k)*x), with T(0, 0) = 1.

EXAMPLE

Triangle begins as:

  1;

  1, -1;

  1, -2,  1;

  1, -3,  3, -1;

  1, -4,  6, -4,  1;

  1, -8, 22,-28, 17, -4;

MATHEMATICA

A049614[n_]:= n!/Product[Prime[i], {i, 1, PrimePi[n]}];

Join[{{1}}, Table[CoefficientList[Product[1 - A049614[k]*x, {k, 0, n}], x], {n, 0, 12}]]//Flatten

PROG

(Sage)

def A049614(n): return factorial(n)/product( nth_prime(j) for j in (1..prime_pi(n)) )

[1]+flatten([[( product(1 - A049614(k)*x for k in (0..n)) ).series(x, n+2).list()[k] for k in (0..n+1)] for n in (0..12)]) # G. C. Greubel, Feb 05 2021

CROSSREFS

Cf. A008275, A034386, A049614, A119490.

Sequence in context: A034253 A203952 A296115 * A281587 A026022 A073714

Adjacent sequences:  A118684 A118685 A118686 * A118688 A118689 A118690

KEYWORD

sign,tabl,less

AUTHOR

Roger L. Bagula, May 20 2006

EXTENSIONS

Edited by G. C. Greubel, Feb 05 2021

STATUS

approved

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Last modified June 14 05:51 EDT 2021. Contains 345018 sequences. (Running on oeis4.)