cp's OEIS Frontend

A385960 Decimal expansion of the absolute value of the coefficient [x^2] Gamma(x).

%I A385960 #14 Jul 15 2025 05:44:32
%S A385960 9,0,7,4,7,9,0,7,6,0,8,0,8,8,6,2,8,9,0,1,6,5,6,0,1,6,7,3,5,6,2,7,5,1,
%T A385960 1,4,9,2,8,6,1,1,4,4,9,0,7,2,5,6,3,7,6,0,9,4,1,3,3,1,1,5,4,0,5,0,4,6,
%U A385960 5,1,8,2,3,7,2,2,3,0,6,9,3,9,8,3,8,7,5,2,7,4,1,1,3,6,2,9,7,7,2,1,6,8,2,1
%N A385960 Decimal expansion of the absolute value of the coefficient [x^2] Gamma(x).
%C A385960 The Laurent series Gamma(x)  = 1/x + Sum_{i>=0} a_i x^i starts with a_0 = -gamma = -A001620, a_1 = A090998 , and a_2 = -0.90747907.. , absolute value here. Recurrence (i+1)*a_i = -gamma *a_{i-1} + Sum_{k=2..i+1} (-1)^k*zeta(k)a_{i-k} .
%H A385960 I. S. Gradsteyn, I. M. Ryzhik, <a href="https://doi.org/10.1016/C2010-0-64839-5">Tables of Series and Products</a>, Academic Press (2014) 8.321.1
%H A385960 R. J. Mathar, <a href="https://vixra.org/abs/2507.0094">Erratum to Exercise A4.2 in "An Introduction to the Theory of the Riemann Zeta Function"</a>, viXra:2507.0094 (2025)
%F A385960 Equals (gamma^3 +3*gamma*zeta(2) +2*zeta(3))/6 , gamma = A001620, zeta(2) = A013661, zeta(3)=A002117.
%e A385960 0.9074790760808862890165601673...
%p A385960 (gamma^3+3*gamma*Zeta(2)+2*Zeta(3))/6 ; evalf(%) ;
%o A385960 (PARI) polcoef(gamma(x), 2) \\ _Michel Marcus_, Jul 13 2025
%Y A385960 Cf. A090998 [x^1], A385961 [x^3], A385962 [x^4].
%K A385960 nonn,cons
%O A385960 0,1
%A A385960 _R. J. Mathar_, Jul 13 2025