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A119724 Generalized Pascal's triangle made using Mod[(Prime[n] - 1)/2, 4] == 2 primorial-like Stirling polynomials. 1
1, 1, -1, 1, -2, 1, 1, -3, 3, -1, 1, -4, 6, -4, 1, 1, -5, 10, -10, 5, -1, 1, -10, 35, -60, 55, -26, 5, 1, -15, 85, -235, 355, -301, 135, -25, 1, -20, 160, -660, 1530, -2076, 1640, -700, 125, 1, -25, 260, -1460, 4830, -9726, 12020, -8900, 3625, -625, 1, -30, 385, -2760, 12130, -33876, 60650, -69000, 48125, -18750 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Apparently the sequence is based on the list of primes p=5, 13, 29, 37, 53, 61,... for which (p-1)/2 == 2 (mod 4), derived from A005097. The coefficients of the polynomial of degree n are listed in row n, where the polynomial is a product of the form prod_i (1-p_i*x), and p_i is the largest prime of that modular subset which is less than i. - R. J. Mathar, May 15 2013

LINKS

Table of n, a(n) for n=0..64.

FORMULA

a(n) = Flatten[Join[{{1}}, Table[Reverse[CoefficientList[Product[x - p1[n], {n, 0, m}], x]], {m, 0, 10}]]]

EXAMPLE

1;   # 1

1, -1; # 1-x

1, -2, 1; # (1-x)^2

1, -3, 3, -1; # (1-x)^3

1, -4, 6, -4, 1;  # (1-x)^4

1, -5, 10, -10, 5, -1;  # (1-x)^5

1, -10, 35, -60, 55, -26, 5;  # (1-x)^5*(1-5x)

1, -15, 85, -235, 355, -301, 135, -25;  # (1-x)^5*(1-5x)^2

1, -20, 160, -660, 1530, -2076, 1640, -700, 125; # (1-x)^5*(1-5x)^3

1, -25, 260, -1460, 4830, -9726, 12020, -8900, 3625, -625; # (1-x)^5*(1-5x)^4

1, -30, 385, -2760, 12130, -33876, 60650, -69000, 48125, -18750,..  # (1-x)^5*(1-5x)^5

MATHEMATICA

a = Join[{{1}}, Table[Reverse[ CoefficientList[Product[x - p1[n], {n, 0, m}], x]], {m, 0, 10}]] aout = Flatten[a]

CROSSREFS

Cf. A007318, A118686.

Sequence in context: A076831 A197061 A230861 * A162424 A008571 A230860

Adjacent sequences:  A119721 A119722 A119723 * A119725 A119726 A119727

KEYWORD

sign,uned,tabf,obsc

AUTHOR

Roger L. Bagula Jun 14 2006

EXTENSIONS

Should be edited in the same way that I edited A118686. Unfortunately p1 has not been defined, but must be related to "Mod[(Prime[n] - 1)/2, 4] == 2". Compare the definition of p[n] in A118686. - N. J. A. Sloane, Oct 08 2006

STATUS

approved

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Last modified February 18 23:26 EST 2018. Contains 299330 sequences. (Running on oeis4.)