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A385962 Decimal expansion of the absolute value of the coefficient [x^4] Gamma(x).

%I A385962 #10 Jul 15 2025 05:46:46
%S A385962 9,8,1,9,9,5,0,6,8,9,0,3,1,4,5,2,0,2,1,0,4,7,0,1,4,1,3,7,9,1,3,7,4,6,
%T A385962 7,5,5,1,7,4,2,6,5,0,7,1,4,7,1,9,8,9,3,0,4,9,9,9,6,7,1,9,0,4,8,8,0,0,
%U A385962 6,3,6,4,9,6,4,0,5,0,0,4,4,6,9,5,9,4,0,5,1,0,2,3,4,7,4,6,8,2,0,6,6,3,2,3,3,2,1,2,5,9,4,6
%N A385962 Decimal expansion of the absolute value of the coefficient [x^4] Gamma(x).
%C A385962 The Laurent series Gamma(x)  = 1/x + Sum_{i>=0} a_i x^i starts with a_0 = -gamma = -A001620, a_1 = A090998 . a_4 = -0.98199506.. , absolute value here.
%H A385962 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 gives recurrence.
%F A385962 Equals (gamma^5 +10*gamma^3*zeta(2) +20*gamma^2*zeta(3) +15*(zeta(2)^2+2*zeta(4))*gamma +20*zeta(2)*zeta(3) +24*zeta(5))/120 , gamma = A001620, zeta(2) = A013661, zeta(3)=A002117, zeta(4) = A013662, zeta(5) = A013663.
%e A385962 0.9819950689031452021047014137..
%p A385962 (gamma^5 +10*gamma^3*Zeta(2) +20*gamma^2*Zeta(3) +15*(Zeta(2)^2+2*Zeta(4))*gamma +20*Zeta(2)*Zeta(3) +24*Zeta(5))/120 ; evalf(%) ;
%Y A385962 Cf. A090998 [x^1], A385960 [x^2], A385961 [x^3].
%K A385962 nonn,cons
%O A385962 0,1
%A A385962 _R. J. Mathar_, Jul 13 2025