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A225116 a(n) = 3^n*A_{n, 1/3}(-1) where A_{n, k}(x) are the generalized Eulerian polynomials. 2
1, 5, 24, 110, 480, 2000, 8064, 32240, 130560, 531200, 2095104, 8030720, 33546240, 156569600, 536838144, 243660800, 8589803520, 244224819200, 137438429184, -28539130347520, 2199021158400, 4960294141952000, 35184363700224, -1015283149035274240, 562949919866880 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..24.

Peter Luschny, Generalized Eulerian polynomials.

FORMULA

a(n) = 2^(1+n)*(3^n+sum_{j=0..n}(binomial(n,j)*Li_{-j}(-1)*3^(n-j))).

a(n) = 2^(t+1)*(zeta(-t)*(1-2^(t+1))+(2^t-1)). - Peter Luschny, Jul 20 2013

MAPLE

EulerianPolynomial := proc(n, k, x) local j; if x = 1 then k^n*n! else (1-x)^(1+n)*(1+add(binomial(n, j)* polylog(-j, x)*k^j, j = 0..n)) fi end:

A225116 := n -> 3^n*EulerianPolynomial(n, 1/3, -1);

seq(round(evalf(A225116(i), 24)), i = 0..24);

MATHEMATICA

Table[2^(t+1)*(Zeta[-t]*(1-2^(t+1))+(2^t-1)), {t, 0, 24}] (* Peter Luschny, Jul 20 2013 *)

Table[EulerE[n, 3] 2^n , {n, 0, 20}] (* Vladimir Reshetnikov, Oct 21 2015 *)

PROG

(Sage)

from mpmath import *

mp.dps = 32; mp.pretty = True

def A225116(n): return 2^(1+n)*(3^n+add(binomial(n, j)*polylog(-j, -1) *3^(n-j) for j in (0..n)))

[A225116(n) for n in (0..24)]

CROSSREFS

Cf. A155585(n) = 1^n*A_{n, 1/1}(-1), A119881(n) = 2^n*A_{n, 1/2}(-1).

Sequence in context: A000953 A183934 A171310 * A081104 A079028 A218987

Adjacent sequences:  A225113 A225114 A225115 * A225117 A225118 A225119

KEYWORD

sign

AUTHOR

Peter Luschny, Apr 29 2013

STATUS

approved

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Last modified June 27 15:12 EDT 2017. Contains 288790 sequences.