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 A264120 Values of k such that A001163(k) is positive. 0
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS 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 LINKS FORMULA a(1) = 0. Conjecture: for n > 1, a(n) = ((-1)^n + 4*n - 7)/2. MATHEMATICA 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&]] PROG (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 CROSSREFS Cf. A001163, A042963. Sequence in context: A188258 A308395 A227149 * A042963 A327220 A166097 Adjacent sequences: A264117 A264118 A264119 * A264121 A264122 A264123 KEYWORD nonn AUTHOR Vladimir Reshetnikov, Nov 03 2015 STATUS approved

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Last modified March 31 21:40 EDT 2023. Contains 361673 sequences. (Running on oeis4.)