A122911 Expansion of (1+x)*(1-6*x-25*x^2)/((1+2x)(1-4x)(1+8x)(1-16x)).

1, 5, 139, 1645, 30506, 452860, 7520584, 118102640, 1907343136, 30375432640, 487141579904, 7785180808960, 124635539862016, 1993587347102720, 31902047417780224, 510395557925908480, 8166626525501136896

Offset

0,2

Comments

Let M be the matrix M(n,k)=J(k+1)*sum{j=0..n, (-1)^(n-j)C(n,j)C(j+1,k+1)}. a(n) gives the row sums of M^4.

Links

Table of n, a(n) for n=0..16.

Index entries for linear recurrences with constant coefficients, signature (10,120,-320,-1024).

Formula

G.f.: (1-5x-31x^2-25x^3)/(1-10x-120x^2+320x^3+1024x^4); a(n)=85*16^n/192+203*(-8)^n/576+55*4^n/288+(-2)^n/72; a(n)=a(n)=J(n)*A122910(n-1)+J(n+1)*A122910(n) where J(n) are the Jacobsthal numbers A001045(n).

Mathematica

CoefficientList[Series[(1+x)(1-6x-25x^2)/((1+2x)(1-4x)(1+8x)(1-16x)), {x, 0, 20}], x] (* or *) LinearRecurrence[{10, 120, -320, -1024}, {1, 5, 139, 1645}, 20] (* Harvey P. Dale, Dec 04 2017 *)

Crossrefs

Sequence in context: A192644 A134766 A224826 * A103235 A188451 A362993

Adjacent sequences: A122908 A122909 A122910 * A122912 A122913 A122914

Keyword

easy,nonn

Author

Paul Barry, Sep 18 2006

Status

approved