A091596 - OEIS

A091596

Expansion of x*(1-2*x^2)/(1-x-2*x^2)^2.

0, 1, 2, 5, 12, 27, 62, 137, 304, 663, 1442, 3109, 6676, 14259, 30342, 64321, 135928, 286415, 601962, 1262173, 2640860, 5514731, 11495502, 23923065, 49710272, 103148807, 213754162, 442421397, 914668964, 1888990243, 3897285142, 8033179569, 16543577736, 34041592639

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OFFSET

0,3

COMMENTS

Second column of A091595.

LINKS

Table of n, a(n) for n=0..33.

Index entries for linear recurrences with constant coefficients, signature (2,3,-4,-4).

FORMULA

From Amiram Eldar, Jan 18 2026: (Start)

a(n) = ((3*n + 8)*2^n + (3*n - 8)*(-1)^n) / 27.

E.g.f.: ((6*x+8)*exp(2*x) - (3*x+8)*exp(-x))/27. (End)

MATHEMATICA

CoefficientList[Series[x (1-2x^2)/(1-x-2x^2)^2, {x, 0, 30}], x] (* or *) LinearRecurrence[{2, 3, -4, -4}, {0, 1, 2, 5}, 40] (* Harvey P. Dale, Dec 01 2015 *)

CROSSREFS

Cf. A091595.

Sequence in context: A086589 A299270 A190171 * A077863 A319172 A018009

Adjacent sequences: A091593 A091594 A091595 * A091597 A091598 A091599

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Jan 23 2004

STATUS

approved