A270307 Expansion of -(4*x^3+8*x^2+4*x+1)/(2*x^4+4*x^3+2*x^2-x-1).

1, 3, 7, 7, 21, 27, 57, 95, 169, 303, 529, 943, 1665, 2943, 5217, 9215, 16321, 28863, 51073, 90367, 159873, 282879, 500481, 885503, 1566721, 2771967, 4904449, 8677375, 15352833, 27163647, 48060417, 85032959, 150448129, 266186751, 470962177

Offset

0,2

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (-1, 2, 4, 2).

Formula

a(n) = (n+1)*Sum_{k=0..n}(Sum_{l=0..n-k}(binomial(k+1,l)*2^l*(-1)^(n-l-k)*binomial(n-2*l,n-l-k))/(k+1)).

Mathematica

LinearRecurrence[{-1, 2, 4, 2}, {1, 3, 7, 7}, 50] (* Harvey P. Dale, Apr 11 2017 *)

Prog

(Maxima)
a(n):=(n+1)*sum(sum(binomial(k+1, l)*2^l*(-1)^(n-l-k)*binomial(n-2*l, n-l-k), l, 0, n-k)/(k+1), k, 0, n);

Crossrefs

Cf. A001405.

Sequence in context: A212286 A157102 A226512 * A261480 A121172 A341539

Adjacent sequences: A270304 A270305 A270306 * A270308 A270309 A270310

Keyword

nonn

Author

Vladimir Kruchinin, Mar 15 2016

Status

approved