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Search: id:A143506
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| A143506 |
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The LerchPhi version of MacMahon numbers (A060187) with the McMullen's transform substitution:x->x+1/x: p(x,n) = 2^n*(1 - x)^(1 + n)LerchPhi[x, -n, 1/2]; q(x,n)=x^(n)*p(x+1/x,n). |
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1
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| 1, 1, 1, 1, 6, 3, 6, 1, 1, 23, 26, 47, 26, 23, 1, 1, 76, 234, 304, 467, 304, 234, 76, 1, 1, 237, 1687, 2630, 5293, 4787, 5293, 2630, 1687, 237, 1, 1, 722, 10549, 27158, 52730, 78586, 84365, 78586, 52730, 27158, 10549, 722, 1, 1, 2179, 60664, 272797, 563029, 1132234
(list; graph; listen)
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OFFSET
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1,5
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COMMENT
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Row sums are:
{3, 17, 147, 1697, 24483, 423857, 8560947, 197613377, 5131725123, 148070287697}.
There should be a one at the beginning of this like in the Eulerian numbers version.
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FORMULA
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p(x,n) = 2^n*(1 - x)^(1 + n)LerchPhi[x, -n, 1/2]; q(x,n)=x^(n)*p(x+1/x,n); t(n,m)=Coefficients(q(x,n)).
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EXAMPLE
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{1, 1, 1},
{1, 6, 3, 6, 1},
{1, 23, 26, 47, 26, 23, 1},
{1, 76, 234, 304, 467, 304, 234, 76, 1},
{1, 237, 1687, 2630, 5293, 4787, 5293, 2630, 1687, 237, 1},
{1, 722, 10549, 27158, 52730, 78586, 84365, 78586, 52730, 27158, 10549, 722, 1},
{1, 2179, 60664, 272797, 563029, 1132234, 1387953, 1723233, 1387953, 1132234, 563029, 272797, 60664, 2179, 1},
{1, 6552, 331620, 2531152, 6664714, 15049320, 24005904, 32544616, 35345619, 32544616, 24005904, 15049320, 6664714, 2531152, 331620, 6552, 1},
{1, 19673, 1756349, 21865356, 81707710, 200211970, 405657666, 606130784, 820748555, 855528995, 820748555, 606130784, 405657666, 200211970, 81707710, 21865356, 1756349, 19673, 1},
{1, 59038, 9116151, 178832246, 979852455, 2777324164, 6603715042, 11563041420, 17751162605, 22053856858, 24236367737, 22053856858, 17751162605, 11563041420, 6603715042, 2777324164, 979852455, 178832246, 9116151, 59038, 1}
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MATHEMATICA
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p[x_, n_] = 2^n*(1 - x)^(1 + n)*LerchPhi[x, -n, 1/2]; Table[FullSimplify[ExpandAll[x^n*p[x + 1/x, n]]], {n, 1, 10}]; Table[CoefficientList[FullSimplify[ExpandAll[x^(n )*p[x + 1/x, n]]], x], {n, 1, 10}]; Flatten[%]
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CROSSREFS
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Cf. A008292, A060187.
Sequence in context: A085653 A022462 A019151 this_sequence A008567 A165065 A069938
Adjacent sequences: A143503 A143504 A143505 this_sequence A143507 A143508 A143509
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KEYWORD
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nonn,uned,probation
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AUTHOR
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Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Oct 25 2008
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