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A147880
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A Fernandez-type expansion for Mallow's A005229: p(x,n)=Product[x+A005229[n],{n,0,Infinity}]; a(n)=Coefficients[(p(x,n)).
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1, 1, 1, 3, 5, 8, 12, 21, 30, 50, 75, 110, 169, 249, 361, 539, 757, 1076, 1583, 2207, 3121, 4415, 6184, 8468, 11775, 16274, 22314, 30601, 41745, 56412, 77008, 103507, 138383, 186928, 249855, 333375, 443898, 588402, 778276, 1031126, 1356945, 1780645
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| The resulting polynomial is equivalent to and 1/q(x) type expansion of q(x)=x^n*f(1/x) and that expansion has a limiting ratio ( largest positive root) near:1.225067086465817 or smaller
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FORMULA
| p(x,n)=Product[x+A005229[n],{n,0,Infinity}]; a(n)=Coefficients[(p(x,n)).
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MATHEMATICA
| (*A005229*) f[n_Integer?Positive] := f[n] = f[ f[n - 2]] + f[n - f[n - 2]]; f[0] = 0; f[1] = f[2] = 1; P[x_, n_] := P[x, n] = Product[1 + f[m] *x^m, {m, 0, n}]; a2 = CoefficientList[ExpandAll[P[x, 100]], x]; Table[a2[[n]], {n, 1, 100}]
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CROSSREFS
| A005229, A147559, A147654, A147655, A004001, A147665
Sequence in context: A004398 A055606 A147879 * A020643 A131354 A092360
Adjacent sequences: A147877 A147878 A147879 * A147881 A147882 A147883
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KEYWORD
| nonn
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Nov 16 2008
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