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Search: id:A154594
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| A154594 |
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A triangle sequence of polynomial coefficients:{a, b, c, d} = {3, 2, 2, 0}; p(x,n)=(-1)^(n)*(1 - d - c x)^(n + 1)*Sum[(a*k + b)^n*(c*x + d)^k, {k, 0, Infinity}]. |
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+0
2
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| 1, -2, -2, 4, 26, 4, -8, -186, -240, -8, 16, 1090, 4524, 2008, 16, -32, -5866, -57992, -85424, -16288, -32, 64, 30354, 616452, 2099504, 1423968, 130848, 64, -128, -154202, -5902944, -39122296, -61925632, -22159968, -1048064, -128, 256
(list; table; graph; listen)
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OFFSET
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0,2
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COMMENT
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This result is from a scan of {a,b,c,d} that are quadratic symmetric.
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FORMULA
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{a, b, c, d} = {3, 2, 2, 0};
p(x,n)=(-1)^(n)*(1 - d - c x)^(n + 1)*Sum[(a*k + b)^n*(c*x + d)^k, {k, 0, Infinity}];
t(n,m)=coefficients(p(x,n)).
p(x,n)=(-2)^n *(1 - 2 x)^(1 + n)* LerchPhi[2 x, -n, 2/3]
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EXAMPLE
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{1},
{-2, -2},
{4, 26, 4},
{-8, -186, -240, -8},
{16, 1090, 4524, 2008, 16},
{-32, -5866, -57992, -85424, -16288, -32},
{64, 30354, 616452, 2099504, 1423968, 130848, 64},
{-128, -154202, -5902944, -39122296, -61925632, -22159968, -1048064, -128},
{256, 776642, 53083228, 619239464, 1884138544, 1615232096, 331200832, 8387456, 256},
{-512, -3896010, -458838072, -8828796768, -46193602464, -76446547776, -38928658560, -4829723136, -67106304, -512},
{1024, 19508722, 3865505076, 117305639616, 982204711680, 2777786591040, 2766183413376, 889656803328, 69360887808, 536865280, 1024}
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MATHEMATICA
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Clear[p, a, b, c, d, n];
{a, b, c, d} = {3, 2, 2, 0};
p[x_, n_] = (-1)^(n)*(1 - d - c x)^(n + 1)*Sum[(a*k + b)^n*(c*x + d)^k, {k, 0, Infinity}];
Table[FullSimplify[ExpandAll[p[x, n]]], {n, 0, 10}];
Table[CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x], {n, 0, 10}];
Flatten[%]
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CROSSREFS
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Row sums are in A151919.
Sequence in context: A128501 A009541 A006829 this_sequence A098335 A049147 A067068
Adjacent sequences: A154591 A154592 A154593 this_sequence A154595 A154596 A154597
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KEYWORD
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sign,tabl,uned
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jan 12 2009
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