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A122610
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Triangle read by rows: T(n,k) is coefficient of x^k in Sum_{m=0..n} x^m*(1-x)^(n-m)*(-1)^[(m+1)/2]*binomial(m-[(m+1)/2],[m/2]).
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2
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1, 1, -2, 1, -3, 1, 1, -4, 3, 1, 1, -5, 6, 1, -2, 1, -6, 10, -1, -6, 1, 1, -7, 15, -6, -11, 6, 1, 1, -8, 21, -15, -15, 18, 1, -2, 1, -9, 28, -29, -15, 39, -6, -9, 1, 1, -10, 36, -49, -7, 69, -30, -21, 9, 1, 1, -11, 45, -76, 14, 105, -84, -30, 36, 1, -2, 1, -12, 55, -111, 54, 140, -182, -15, 96, -14, -12, 1, 1, -13, 66, -155
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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REFERENCES
| P. Steinbach, Golden fields: a case for the heptagon, Math. Mag. 70 (1997), no. 1, 22-31.
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EXAMPLE
| 1
1, -2
1,-3, 1
1, -4, 3, 1
1, -5, 6, 1,-2
1, -6, 10,-1, -6, 1
1, -7, 15, -6, -11, 6, 1
1,-8, 21, -15, -15, 18, 1, -2
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MATHEMATICA
| T[n_, k_] := (-1)^Floor[(k + 1)/2]*Binomial[n - Floor[(k + 1)/2], Floor[k/2]] a = Table[CoefficientList[Sum[T[n, k]*p^k*(1 - p)^(n -k), {k, 0, n}], p], {n, 0, 10}]; Flatten[a]
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PROG
| (PARI) {T(n, k)=local(A); if(k<0|k>n, 0, A=sum(k=0, n, x^k*(1-x)^(n-k)*(-1)^((k+1)\2)*binomial(n-((k+1)\2), k\2)); polcoeff(A, k))}
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CROSSREFS
| Cf. A066170.
Sequence in context: A138151 A166556 A143318 * A011973 A115139 A198788
Adjacent sequences: A122607 A122608 A122609 * A122611 A122612 A122613
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KEYWORD
| sign,tabl
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AUTHOR
| Roger Bagula and Gary Adamson (rlbagulatftn(AT)yahoo.com), Sep 20 2006
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EXTENSIONS
| Edited by N. J. A. Sloane (njas(AT)research.att.com), Sep 24 2006
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