A122910 -id:A122910 - cp's OEIS frontend

A122911 Expansion of (1+x)(1-6x-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

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Paul Barry, Sep 18 2006

easy
nonn

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.

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

Cf. A001045, A122910.

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 *)

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) = J(n)*A122910(n-1)+J(n+1)*A122910(n) where J(n) are the Jacobsthal numbers A001045(n).

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

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cp's OEIS Frontend

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

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