A264120 Values of k such that A001163(k) is positive.

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

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

Table of n, a(n) for n=1..63.

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