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A156857 Expansion of (1+2*x)/(1+x+4*x^2)^2. 1
1, 0, -9, 10, 45, -108, -125, 702, -135, -3320, 4239, 11250, -31931, -18180, 165915, -92762, -651375, 1101168, 1747495, -6710310, -694179, 30182500, -28394829, -101934450, 229069225, 203510232, -1198850625, 364506562, 4767453045 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
Hankel transform of A091526.
LINKS
FORMULA
G.f.: (1 +2*x)/(1 +2*x +9*x^2 +8*x^3 +16*x^4).
a(n) = (-2)*Sum_{j=0..n} ChebyshevU(n-j, 1/4)*(ChebyshevU(j, 1/4) - ChebyshevU(j-1, 1/4)). - G. C. Greubel, Jan 28 2022
MATHEMATICA
LinearRecurrence[{-2, -9, -8, -16}, {1, 0, -9, 10}, 41] (* or *)
A156857[n_]:= (-2)^n*Sum[ChebyshevU[n-j, 1/4]*(ChebyshevU[j, 1/4] - ChebyshevU[j-1, 1/4]), {j, 0, n}];
Table[A156857[n], {n, 0, 40}] (* G. C. Greubel, Jan 28 2022 *)
PROG
(Magma) I:=[1, 0, -9, 10]; [n le 4 select I[n] else (-1)*(2*Self(n-1) +9*Self(n-2) +8*Self(n-3) +16*Self(n-4)): n in [1..41]]; // G. C. Greubel, Jan 28 2022
(Sage)
def A156857(n): return (-2)^n*sum( chebyshev_U(n-j, 1/4)*(chebyshev_U(j, 1/4) - chebyshev_U(j-1, 1/4)) for j in (0..n))
[A156857(n) for n in (0..40)] # G. C. Greubel, Jan 28 2022
CROSSREFS
Sequence in context: A154389 A041172 A248353 * A259914 A368047 A037954
KEYWORD
easy,sign
AUTHOR
Paul Barry, Feb 17 2009
STATUS
approved

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Last modified March 29 06:15 EDT 2024. Contains 371265 sequences. (Running on oeis4.)