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A087674 Value of the n-th Eulerian polynomial (cf. A008292) evaluated at x=-2. 1
1, 1, -1, -3, 15, 21, -441, 477, 19935, -101979, -1150281, 14838957, 60479055, -2328851979, 3529587879, 403992301437, -3333935426625, -72778393505979, 1413503392326039, 10851976875907917, -554279405351601105, 713848745428080021 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Table of n, a(n) for n=0..21.

FORMULA

a(n) = -3^(n+1)/2*polylog(-n, -2).

E.g.f.: 3*exp(x)/(2*exp(x)+exp(-2*x)).

O.g.f.: Sum_{n>=0} n! * x^n / Product_{k=1..n} (1 + 3*k*x). [Paul D. Hanna, Jul 20 2011]

G.f.: 1/Q(0), where Q(k)= 1 - x*(k+1)/(1 + x*(2*k+2)/Q(k+1)); (continued fraction). - Sergei N. Gladkovskii, May 20 2013

MATHEMATICA

Table[-3^(n+1)/2*PolyLog[-n, -2], {n, 0, 21}] (* Jean-Fran├žois Alcover, Apr 26 2013 *)

PROG

(PARI) {a(n)=polcoeff(sum(m=0, n, m!*x^m/prod(k=1, m, 1+3*k*x+x*O(x^n))), n)} /* Paul D. Hanna, Jul 20 2011 */

(PARI) x='x+O('x^66); Vec(serlaplace( 3*exp(x)/(2*exp(x)+exp(-2*x)) )) \\ Joerg Arndt, Apr 21 2013

CROSSREFS

Cf. A000670.

Sequence in context: A117801 A277585 * A212846 A276804 A009057 A083795

Adjacent sequences:  A087671 A087672 A087673 * A087675 A087676 A087677

KEYWORD

sign

AUTHOR

Vladeta Jovovic, Sep 26 2003

EXTENSIONS

More terms from Paul D. Hanna, Jul 20 2011

STATUS

approved

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Last modified May 23 08:03 EDT 2017. Contains 286909 sequences.