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A248160
Expansion of (1 - 2*x^2)/(1 + x)^5. Fourth column of Riordan triangle A248156.
2
1, -5, 13, -25, 40, -56, 70, -78, 75, -55, 11, 65, -182, 350, -580, 884, -1275, 1767, -2375, 3115, -4004, 5060, -6302, 7750, -9425, 11349, -13545, 16037, -18850, 22010, -25544, 29480, -33847, 38675, -43995, 49839, -56240, 63232, -70850, 79130, -88109, 97825, -108317, 119625, -131790
OFFSET
0,2
COMMENTS
This is the column k=3 sequence of the Riordan triangle A248156 without the leading three zeros.
FORMULA
O.g.f.: (1 - 2*x^2)/(1 + x)^5 = -2/(1 + x)^3 + 4/(1 + x)^4 - 1/(1 + x)^5.
a(n) = (-1)^n*(n+1)*(n+2)*(12 + 9*n - n^2)/4!.
a(n) = -5*(a(n-1) + a(n-4)) - 10*(a(n-2) + a(n-3)) - a(n-5), n >= 5, with a(0) =1, a(1) = -5, a(2) = 13, a(3) = -25 and a(4) = 40.
MAPLE
A248160:=n->(-1)^n*(n+1)*(n+2)*(12 + 9*n - n^2)/4!: seq(A248160(n), n=0..30); # Wesley Ivan Hurt, Oct 09 2014
MATHEMATICA
Table[(-1)^n*(n + 1)*(n + 2)*(12 + 9*n - n^2)/4!, {n, 0, 30}] (* Wesley Ivan Hurt, Oct 09 2014 *)
CoefficientList[Series[(1-2x^2)/(1+x)^5, {x, 0, 50}], x] (* or *) LinearRecurrence[ {-5, -10, -10, -5, -1}, {1, -5, 13, -25, 40}, 50] (* Harvey P. Dale, Apr 13 2019 *)
PROG
(PARI) Vec((1 - 2*x^2)/(1 + x)^5 + O(x^50)) \\ Michel Marcus, Oct 09 2014
CROSSREFS
Cf. A248156, A248157 (k=0), A248158 (k=1), A248159 (k=2).
Sequence in context: A094079 A194811 A112558 * A098972 A081961 A096891
KEYWORD
sign,easy
AUTHOR
Wolfdieter Lang, Oct 09 2014
STATUS
approved