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A219619 a(n) = n! * (n^4 + n^2 + 1). 1
1, 3, 42, 546, 6552, 78120, 959760, 12353040, 167771520, 2410611840, 36654508800, 589291718400, 10002032409600, 178908534604800, 3366215358105600, 66496549287168000, 1376573115101184000, 29810519036153856000, 674176353586864128000, 15896946656727392256000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

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

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.

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

EXAMPLE

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

PROG

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

(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

CROSSREFS

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

Sequence in context: A160874 A003770 A173936 * A097068 A269046 A092470

Adjacent sequences:  A219616 A219617 A219618 * A219620 A219621 A219622

KEYWORD

nonn,easy

AUTHOR

Franz Vrabec, Nov 24 2012

STATUS

approved

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Last modified July 17 21:24 EDT 2019. Contains 325109 sequences. (Running on oeis4.)