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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 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.)