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A179995 Generating function A(5,t)(1+t+t^2)/(1-t)^6, where A(5,t) is an Eulerian polynomial. 0
1, 33, 276, 1299, 4392, 11925, 27708, 57351, 108624, 191817, 320100, 509883, 781176, 1157949, 1668492, 2345775, 3227808, 4358001, 5785524, 7565667, 9760200, 12437733, 15674076, 19552599, 24164592, 29609625, 35995908 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The Eulerian polynomials A(n,t) are here defined in accordance with the Digital Library of Mathematical Functions, Table 26.14.1.

Sums of 3 consecutive fifth powers: a(n) = (n-1)^5+n^5+(n+1)^5. - Bruno Berselli, Jun 24 2013

LINKS

Table of n, a(n) for n=0..26.

OEIS Wiki, Eulerian polynomials.

Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

FORMULA

From Bruno Berselli, Jun 24 2013: (Start)

G.f.: (1 + 27*x + 93*x^2 + 118*x^3 + 93*x^4 + 27*x^5 + x^6) / (1 - x)^6.

a(n) = n*(3*n^4 + 20*n^2 + 10) for n>0, a(0)=1. (End)

a(0)=1, a(1)=33, a(2)=276, a(3)=1299, a(4)=4392, a(5)=11925, a(6)=27708; for n>6, a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6). - Harvey P. Dale, Apr 10 2015

MAPLE

gfA179995 := proc(t) local i;

add([1, 27, 93, 118, 93, 27, 1][i+1]*t^i, i=0..5)/(1-t)^6 end:

seq(coeff(series(gfA179995(t), t, 24), t, j), j=0..16);

MATHEMATICA

Join[{1}, Table[n (3 n^4 + 20 n^2 + 10), {n, 30}]] (* Bruno Berselli, Jun 24 2013 *)

LinearRecurrence[{6, -15, 20, -15, 6, -1}, {1, 33, 276, 1299, 4392, 11925, 27708}, 30] (* Harvey P. Dale, Apr 10 2015 *)

PROG

(MAGMA) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((1+27*x+93*x^2+118*x^3+93*x^4+27*x^5+x^6)/(1-x)^6)); // Bruno Berselli, Jun 24 2013

CROSSREFS

Cf. A158799, A008486, A005918, A027602, A160827 which have generating functions of type A(n, t)(1+t+t^2)/(1-t)^(n+1).

Sequence in context: A252978 A268264 A008515 * A000539 A023874 A265839

Adjacent sequences:  A179992 A179993 A179994 * A179996 A179997 A179998

KEYWORD

nonn,easy

AUTHOR

Peter Luschny, Aug 05 2010

STATUS

approved

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Last modified August 19 13:00 EDT 2017. Contains 290807 sequences.