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A264120
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Values of k such that A001163(k) is positive.
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0
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0, 1, 2, 5, 6, 9, 10, 13, 14, 17, 18, 21, 22, 25, 26, 29, 30, 33, 34, 37, 38, 41, 42, 45, 46, 49, 50, 53, 54, 57, 58, 61, 62, 65, 66, 69, 70, 73, 74, 77, 78, 81, 82, 85, 86, 89, 90, 93, 94, 97, 98, 101, 102, 105, 106, 109, 110, 113, 114, 117, 118, 121, 122
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OFFSET
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1,3
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COMMENTS
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Indices of positive terms in Stirling's asymptotic expansion of the Gamma-function.
If the conjecture is true, this entry will be removed as a duplicate of A042963. - R. J. Mathar, Nov 06 2015
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LINKS
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Table of n, a(n) for n=1..63.
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FORMULA
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a(1) = 0.
Conjecture: for n > 1, a(n) = ((-1)^n + 4*n - 7)/2.
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MATHEMATICA
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Module[{a}, a[0] = 1; a[n_] := a[n] = (a[n-1]/n - Sum[a[k] a[n-k]/(k+1), {k, 1, n-1}])/(1+1/(n+1)); Select[Range[0, 200], a[2#]>0&]]
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PROG
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(PARI) a(k) = local(A, m); if(k<1, k==0, A=vector(m=2*k+1, t, 1); for(t=2, m, A[t]=(A[t-1]-sum(i=2, t-1, i*A[i]*A[t+1-i]))/(t+1)); numerator(A[m]*m!/2^k/k!))
for(k=0, 100, if(a(k) > 0, print1(k", "))) \\ Altug Alkan, Nov 04 2015
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CROSSREFS
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Cf. A001163, A042963.
Sequence in context: A188258 A308395 A227149 * A042963 A327220 A166097
Adjacent sequences: A264117 A264118 A264119 * A264121 A264122 A264123
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KEYWORD
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nonn
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AUTHOR
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Vladimir Reshetnikov, Nov 03 2015
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STATUS
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approved
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