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

1, 3, 42, 546, 6552, 78120, 959760, 12353040, 167771520, 2410611840, 36654508800, 589291718400, 10002032409600, 178908534604800, 3366215358105600, 66496549287168000, 1376573115101184000, 29810519036153856000, 674176353586864128000, 15896946656727392256000

Offset: 0

Author

Franz Vrabec, Nov 24 2012

Keywords

• nonn
• easy

Comments

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

Examples

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

Links

• Iain Fox, Table of n, a(n) for n = 0..445
• G. I. Senum, A Series for e, Problem E3352, Amer. Math. Monthly 98 (1991), No. 4, pp. 369-370.

Crossrefs

Cf. A000142 (n!), A059826 (n^4 + n^2 + 1).

Programs

Mathematica

Array[#!*(#^4 + #^2 + 1) &, 20, 0] (* Michael De Vlieger, Jan 29 2021 *)
nmax = 20; CoefficientList[Series[(1 - 2*x + 16*x^2 + 6*x^3 + 3*x^4) / (1 - x)^5, {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Jan 29 2021 *)

PARI

a(n) = n! * (n^4 + n^2 + 1); \\ Michel Marcus, Nov 19 2017

PARI

first(n) = { my(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

Formula

a(n) = A000142(n)*A059826(n). - Michel Marcus, Nov 19 2017

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