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A176160
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A polynomial coefficient sequence:p(x,n,m)=(1 + 4*Binomial[n, m]*x)^n
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0
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1, 5, 5, 25, 81, 25, 125, 2197, 2197, 125, 625, 83521, 390625, 83521, 625, 3125, 4084101, 115856201, 115856201, 4084101, 3125, 15625, 244140625, 51520374361, 282429536481, 51520374361, 244140625, 15625, 78125, 17249876309
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OFFSET
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0,2
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COMMENTS
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Row sums are:
{1, 10, 131, 4644, 558917, 239886854, 385958597703, 2280119446470280, 52063212260725437065, 4384388899674032467912458, 1449048908960986942519336016459,...}.
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LINKS
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FORMULA
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p(x,n,m)=(1 + 4*Binomial[n, m]*x)^n
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EXAMPLE
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{1},
{5, 5},
{25, 81, 25},
{125, 2197, 2197, 125},
{625, 83521, 390625, 83521, 625},
{3125, 4084101, 115856201, 115856201, 4084101, 3125},
{15625, 244140625, 51520374361, 282429536481, 51520374361, 244140625, 15625},
{78125, 17249876309, 32057708828125, 1107984764452581, 1107984764452581, 32057708828125, 17249876309, 78125},
{390625, 1406408618241, 26584441929064321, 6568408355712890625, 38873223852623509441, 6568408355712890625, 26584441929064321, 1406408618241, 390625},
{1953125, 129961739795077, 28334269484119140625, 56062067225927988301777, 2136104048211642384765625, 2136104048211642384765625, 56062067225927988301777, 28334269484119140625, 129961739795077, 1953125},
{9765625, 13422659310152401, 37738596846955704499801, 662904189510194816788612801, 176994576151109753197786640401, 1093733872802526507260136674401, 176994576151109753197786640401, 662904189510194816788612801, 37738596846955704499801, 13422659310152401, 9765625}
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MATHEMATICA
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Clear[p, n, m];
p[x_, n_, m_] := (1 + 4*Binomial[n, m]*x)^n;
Table[Table[ Apply[Plus, CoefficientList[p[x, n, m], x]], {m, 0, n}], {n, 0, 10}];
Flatten[%]
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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