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URL: https://oeis.org/A391833

⇱ A391833 - OEIS

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A391833
a(n) = (1/4) * Sum_{k=0..floor(n/2)} (k+2) * 2^k * binomial(2*k+2,2*n-4*k+1).
3
1, 0, 6, 6, 24, 80, 104, 560, 800, 2960, 6720, 15200, 46384, 90944, 273184, 601248, 1525760, 3863552, 8808192, 23230464, 53175296, 134251008, 323028992, 774392832, 1920513280, 4529858560, 11176308224, 26669133312, 64509908992, 156109492224, 372930435072, 904840884224, 2160718012416
OFFSET
0,3
LINKS
Index entries for linear recurrences with constant coefficients, signature (0,8,8,-24,-16,8,-32,-48,96,-96,64,-16).
FORMULA
G.f.: (1-2*x^2-2*x^3) / ((1-2*x^2-2*x^3)^2 - 16*x^5)^2.
a(n) = 8*a(n-2) + 8*a(n-3) - 24*a(n-4) - 16*a(n-5) + 8*a(n-6) - 32*a(n-7) - 48*a(n-8) + 96*a(n-9) - 96*a(n-10) + 64*a(n-11) - 16*a(n-12).
MATHEMATICA
CoefficientList[Series[(1-2*x^2-2*x^3)/((1-2*x^2-2*x^3)^2-16*x^5)^2, {x, 0, 40}], x] (* Vincenzo Librandi, Jan 03 2026 *)
PROG
(PARI) my(N=40, x='x+O('x^N)); Vec((1-2*x^2-2*x^3)/((1-2*x^2-2*x^3)^2-16*x^5)^2)
(Magma) m:=40; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R! (1-2*x^2-2*x^3) / ((1-2*x^2-2*x^3)^2 - 16*x^5)^2); // Vincenzo Librandi, Jan 03 2026
CROSSREFS
Sequence in context: A087236 A341267 A219910 * A334569 A077193 A056482
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Dec 21 2025
STATUS
approved