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Search: id:A155864
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| A155864 |
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A sequence of polynomial coefficients related to the Second derivative of the Pascal triangle: p(x,n)=x^n+1+x*d^2(x+1)^(n)/dx^2=If[n == 0, 1, x^n + 1 + x*D[(x + 1)^(n), {x, 2}]]. |
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+0
1
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| 1, 1, 1, 1, 2, 1, 1, 6, 6, 1, 1, 12, 24, 12, 1, 1, 20, 60, 60, 20, 1, 1, 30, 120, 180, 120, 30, 1, 1, 42, 210, 420, 420, 210, 42, 1, 1, 56, 336, 840, 1120, 840, 336, 56, 1, 1, 72, 504, 1512, 2520, 2520, 1512, 504, 72, 1, 1, 90, 720, 2520, 5040, 6300, 5040, 2520, 720, 90, 1
(list; table; graph; listen)
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OFFSET
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0,5
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COMMENT
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Row sums are:
{1, 2, 4, 14, 50, 162, 482, 1346, 3586, 9218, 23042,...}
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FORMULA
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p(x,n)=x^n+1+x*d^2(x+1)^(n)/dx^2
p(x,n)=If[n == 0, 1, x^n + 1 + x*D[(x + 1)^(n), {x, 2}]]
t(n,m)=coefficients(p(x,n))
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EXAMPLE
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{1},
{1, 1},
{1, 2, 1},
{1, 6, 6, 1},
{1, 12, 24, 12, 1},
{1, 20, 60, 60, 20, 1},
{1, 30, 120, 180, 120, 30, 1},
{1, 42, 210, 420, 420, 210, 42, 1},
{1, 56, 336, 840, 1120, 840, 336, 56, 1},
{1, 72, 504, 1512, 2520, 2520, 1512, 504, 72, 1},
{1, 90, 720, 2520, 5040, 6300, 5040, 2520, 720, 90, 1}
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MATHEMATICA
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Clear[p, n, m, x, a];
p[x_, n_] = If[n == 0, 1, x^n + 1 + x*D[(x + 1)^(n), {x, 2}]];
Table[ExpandAll[p[x, n]], {n, 0, 10}];
a = Table[CoefficientList[ExpandAll[p[x, n]], x], {n, 0, 10}];
Flatten[a]
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CROSSREFS
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Sequence in context: A143185 A157635 A075798 this_sequence A145903 A155795 A009963
Adjacent sequences: A155861 A155862 A155863 this_sequence A155865 A155866 A155867
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KEYWORD
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nonn,tabl,uned
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jan 29 2009
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