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A168525 Coefficients of polynomials:a0 = 65/19; b0 = -162/19; c0 = 135/38;; p(x,n)=(a0*(x + 1)^n + b0*((1 - x)^( n + 2))Sum[(1 + k)^(n + 1)* x^k, {k, 0, Infinity}])/(2) + c0*2^n* (1 - x)^(1 + n) LerchPhi[ x, -n, 1/2] 0
19, 19, 19, 19, 146, 19, 19, 759, 759, 19, 19, 3154, 10374, 3154, 19, 19, 11543, 89398, 89398, 11543, 19, 19, 39210, 615669, 1394444, 615669, 39210, 19, 19, 127303, 3747297, 16267301, 16267301, 3747297, 127303, 19, 19, 401858, 21201472 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Row sums are:

{19, 38, 184, 1556, 16720, 201920, 2704240, 40283840, 667344640, 12247216640, 247589428480...}

Linear solution for an {1, 166, 546, 166, 1} quartic level between Pascal, Eulerian and MacMahon numbers.

Factor of 19 is necessary to get all integers for this unexpected rational solution.

A Floor[] gives this near a {1,7,1} quadratic level.

LINKS

Table of n, a(n) for n=0..38.

EXAMPLE

{19},

{19, 19},

{19, 146, 19},

{19, 759, 759, 19},

{19, 3154, 10374, 3154, 19},

{19, 11543, 89398, 89398, 11543, 19},

{19, 39210, 615669, 1394444, 615669, 39210, 19},

{19, 127303, 3747297, 16267301, 16267301, 3747297, 127303, 19},

{19, 401858, 21201472, 160611806, 302914330, 160611806, 21201472, 401858, 19},

{19, 1246167, 114679080, 1428420288, 4579262766, 4579262766, 1428420288, 114679080, 1246167, 19},

{19, 3820474, 602977383, 11856832392, 60428541126, 101805085692, 60428541126, 11856832392, 602977383, 3820474, 19}

MATHEMATICA

a0 = 65/19; b0 = -162/19; c0 = 135/38;

p[x_, n_] = (a0*(x + 1)^n + b0*((1 - x)^(n + 2)) Sum[(1 + k)^(n + 1)*x^k, {k, 0, Infinity}])/( 2) + c0*2^n* (1 - x)^(1 + n) LerchPhi[x, -n, 1/2]

Flatten[Table[19*CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x], {n, 0, 10}]]

CROSSREFS

Cf. A142458, A142459

Sequence in context: A057430 A010858 A291499 * A272897 A040343 A022353

Adjacent sequences:  A168522 A168523 A168524 * A168526 A168527 A168528

KEYWORD

nonn,uned

AUTHOR

Roger L. Bagula, Nov 28 2009

STATUS

approved

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Last modified January 22 02:06 EST 2020. Contains 331133 sequences. (Running on oeis4.)