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%I #30 Jun 17 2023 03:06:25
%S 2,8,9,8,6,8,1,3,3,6,9,6,4,5,2,8,7,2,9,4,4,8,3,0,3,3,3,2,9,2,0,5,0,3,
%T 7,8,4,3,7,8,9,9,8,0,2,4,1,3,5,9,6,8,7,5,4,7,1,1,1,6,4,5,8,7,4,0,0,1,
%U 4,9,4,0,8,0,6,4,0,1,7,4,7,6,6,7,2,5,7,8,0,1,2,3,9
%N Decimal expansion of Sum_{k>=0} (k!/(k+2)!)^2.
%D Alexander Apelblat, Tables of Integrals and Series, Harri Deutsch, (1996), 4.1.31.
%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.19 Vallée's Constant, p. 161.
%H R. J. Mathar, <a href="http://arxiv.org/abs/1301.6293">Tightly circumscribed regular polygons</a>, arXiv:1301.6293 [math.MG], 2013, value (A15).
%F Equals A002388/3-3 = Sum_{n>=1} 1/A002378(n)^2 = Sum_{n>=2} 1/A035287(n).
%e 0.28986813369645287294483...
%p evalf(1/3*Pi^2-3) ;
%t RealDigits[Pi^2/3 - 3, 10, 120][[1]] (* _Amiram Eldar_, Jun 17 2023 *)
%o (PARI) Pi^2/3-3 \\ _Seiichi Manyama_, Dec 09 2021
%o (PARI) sumnumrat(1/(x^4 + 2*x^3 + x^2), 1) \\ _Charles R Greathouse IV_, Jan 20 2022
%Y Cf. A002388 (Pi^2), A002378 (oblong numbers), A035287, A348670.
%K cons,easy,nonn
%O 0,1
%A _R. J. Mathar_, Feb 08 2009
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