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A168622
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Triangle T(n,k) with the coefficient [x^k] of the polynomial 7*(x+1)^n - 6*(x^n+1) in row n, column k. T(0,0)=1.
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0
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1, 1, 1, 1, 14, 1, 1, 21, 21, 1, 1, 28, 42, 28, 1, 1, 35, 70, 70, 35, 1, 1, 42, 105, 140, 105, 42, 1, 1, 49, 147, 245, 245, 147, 49, 1, 1, 56, 196, 392, 490, 392, 196, 56, 1, 1, 63, 252, 588, 882, 882, 588, 252, 63, 1, 1, 70, 315, 840, 1470, 1764, 1470, 840, 315, 70, 1
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OFFSET
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0,5
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COMMENTS
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Row sums are 1, 2, 16, 44, 100, 212, 436, 884, 1780, 3572, 7156,.. apparently entries of A048489 multiplied by 2.
These plus forms generalize sequence A132047.
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LINKS
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EXAMPLE
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1;
1, 1;
1, 14, 1;
1, 21, 21, 1;
1, 28, 42, 28, 1;
1, 35, 70, 70, 35, 1;
1, 42, 105, 140, 105, 42, 1;
1, 49, 147, 245, 245, 147, 49, 1;
1, 56, 196, 392, 490, 392, 196, 56, 1;
1, 63, 252, 588, 882, 882, 588, 252, 63, 1;
1, 70, 315, 840, 1470, 1764, 1470, 840, 315, 70, 1;
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MATHEMATICA
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m = 3; p[x_, n_] := If[n == 0, 1, (2*m + 1)(x + 1)^n - 2*m*(x^n + 1)]
a = Table[CoefficientList[p[x, n], x], {n, 0, 10}];
Flatten[a]
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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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