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A147566 A symmetrical Polynomial set: p(x,n)=If[n >= 0, (x + 1)^(n + 2) + x*((1 + x)^(n) + 2^(n)*(1 - x)^(n + 1)*LerchPhi[x, -n, 1/2]), (x + 1)^(n + 2)], 0
1, 1, 1, 1, 4, 1, 1, 5, 5, 1, 1, 6, 14, 6, 1, 1, 7, 36, 36, 7, 1, 1, 8, 95, 256, 95, 8, 1, 1, 9, 263, 1727, 1727, 263, 9, 1, 1, 10, 756, 10614, 23638, 10614, 756, 10, 1, 1, 11, 2222, 60762, 259884, 259884, 60762, 2222, 11, 1, 1, 12, 6605, 331760, 2485554, 4675336, 2485554 (list; graph; refs; listen; history; text; internal format)
OFFSET

-2,5

COMMENTS

Row sums are: {1, 2, 6, 12, 28, 88, 464, 4000, 46400, 645760, 10323200, 185797120, 3715896320,...}.

LINKS

Table of n, a(n) for n=-2..59.

FORMULA

p(x,n)=If[n >= 0, (x + 1)^(n + 2) + x*((1 + x)^(n) + 2^(n)*(1 - x)^(n + 1)*LerchPhi[x, -n, 1/2]), (x + 1)^(n + 2)]; t(n,m)=coefficients(p(x,n)).

EXAMPLE

{1}, {1, 1}, {1, 4, 1}, {1, 5, 5, 1}, {1, 6, 14, 6, 1}, {1, 7, 36, 36, 7, 1}, {1, 8, 95, 256, 95, 8, 1}, {1, 9, 263, 1727, 1727, 263, 9, 1}, {1, 10, 756, 10614, 23638, 10614, 756, 10, 1}, {1, 11, 2222, 60762, 259884, 259884, 60762, 2222, 11, 1}, {1, 12, 6605, 331760, 2485554, 4675336, 2485554, 331760, 6605, 12, 1}, {1, 13, 19737, 1756541, 21708386, 69413882, 69413882, 21708386, 1756541, 19737, 13, 1}, {1, 14, 59114, 9116406, 178301519, 906924284, 1527093644, 906924284, 178301519, 9116406, 59114, 14, 1}

MATHEMATICA

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

CROSSREFS

Sequence in context: A028275 A173118 A147289 * A204621 A146770 A143334

Adjacent sequences:  A147563 A147564 A147565 * A147567 A147568 A147569

KEYWORD

nonn

AUTHOR

Roger L. Bagula, Nov 07 2008

STATUS

approved

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Last modified October 13 18:57 EDT 2019. Contains 327981 sequences. (Running on oeis4.)