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A147565 Average of Pascal's triangle and MacMahon numbers: p(x,n)=((1 + x)^(n) + 2^(n)*(1 - x)^(n + 1)*LerchPhi[x, -n, 1/2])/2. 0
1, 1, 1, 1, 4, 1, 1, 13, 13, 1, 1, 40, 118, 40, 1, 1, 121, 846, 846, 121, 1, 1, 364, 5279, 11784, 5279, 364, 1, 1, 1093, 30339, 129879, 129879, 30339, 1093, 1, 1, 3280, 165820, 1242672, 2337542, 1242672, 165820, 3280, 1, 1, 9841, 878188, 10854028, 34706710 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row sums are: {1, 2, 6, 28, 200, 1936, 23072, 322624, 5161088, 92897536, 1857946112,...}.

LINKS

Table of n, a(n) for n=0..49.

FORMULA

p(x,n)=((1 + x)^(n) + 2^(n)*(1 - x)^(n + 1)*LerchPhi[x, -n, 1/2])/2; t(n,m)=coefficients(p(x,n)).

EXAMPLE

{1}, {1, 1}, {1, 4, 1}, {1, 13, 13, 1}, {1, 40, 118, 40, 1}, {1, 121, 846, 846, 121, 1}, {1, 364, 5279, 11784, 5279, 364, 1}, {1, 1093, 30339, 129879, 129879, 30339, 1093, 1}, {1, 3280, 165820, 1242672, 2337542, 1242672, 165820, 3280, 1}, {1, 9841, 878188, 10854028, 34706710, 34706710, 10854028, 878188, 9841, 1}, {1, 29524, 4558093, 89150512, 453461746, 763546360, 453461746, 89150512, 4558093, 29524, 1}

MATHEMATICA

Clear[t, p, x, n]; p[x_, n_] = ((1 + x)^(n) + 2^(n)*(1 - x)^(n + 1)*LerchPhi[x, -n, 1/2])/2; Table[CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x], {n, 0, 10}]; Flatten[%]

CROSSREFS

Sequence in context: A152613 A157153 A212801 * A022167 A064281 A267318

Adjacent sequences:  A147562 A147563 A147564 * A147566 A147567 A147568

KEYWORD

nonn

AUTHOR

Roger L. Bagula, Nov 07 2008

STATUS

approved

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Last modified October 24 01:08 EDT 2018. Contains 316541 sequences. (Running on oeis4.)