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A219619 a(n) = n! * (n^4 + n^2 + 1). 1

%I

%S 1,3,42,546,6552,78120,959760,12353040,167771520,2410611840,

%T 36654508800,589291718400,10002032409600,178908534604800,

%U 3366215358105600,66496549287168000,1376573115101184000,29810519036153856000,674176353586864128000,15896946656727392256000

%N a(n) = n! * (n^4 + n^2 + 1).

%C Sum_{n>=0} 1/a(n) = e/2.

%H Iain Fox, <a href="/A219619/b219619.txt">Table of n, a(n) for n = 0..445</a>

%H G. I. Senum, <a href="http://www.jstor.org/stable/2323815">A Series for e, Problem E3352</a>, Amer. Math. Monthly 98 (1991), No. 4, pp. 369-370.

%F a(n) = A000142(n)*A059826(n). - _Michel Marcus_, Nov 19 2017

%F E.g.f.: (3*x^4 - 6*x^3 - 16*x^2 + 2*x - 1)/(x - 1)^5. - _Iain Fox_, Nov 19 2017

%e a(3) = 3!*(3^4 + 3^2 + 1) = 6*91 = 546.

%o (PARI) a(n) = n! * (n^4 + n^2 + 1); \\ _Michel Marcus_, Nov 19 2017

%o (PARI) first(n) = { x='x+O('x^n); Vec(serlaplace((3*x^4-6*x^3-16*x^2+2*x-1)/(x-1)^5)); } \\ _Iain Fox_, Nov 19 2017

%Y Cf. A000142 (n!), A059826 (n^4 + n^2 + 1), A072334 (e^2).

%K nonn,easy

%O 0,2

%A _Franz Vrabec_, Nov 24 2012

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Last modified October 19 03:34 EDT 2019. Contains 328211 sequences. (Running on oeis4.)