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A181474 Sequence related to the Hankel transform of A105523(n+5). 1
1, 2, 10, 15, 42, 56, 120, 150, 275, 330, 546, 637, 980, 1120, 1632, 1836, 2565, 2850, 3850, 4235, 5566, 6072, 7800, 8450, 10647, 11466, 14210, 15225, 18600, 19840, 23936, 25432, 30345, 32130, 37962, 40071, 46930 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
The Hankel transform of A105523(n+5) is (-1)^C(n+2,2)a(n+1).
LINKS
Nathaniel K. Green and Edward D. Kim, Further techniques on a polynomial positivity question of Collins, Dykema, and Torres-Ayala, arXiv:2307.06311 [math.OC], 2023. See p. 18.
FORMULA
G.f.: (1+x+4x^2+x^3+x^4)/((1-x)^5(1+x)^4);
a(n) = 2^n*(n+2)*(n+3)*Gamma(floor(n/2)+3)*Gamma(floor((n+1)/2)+1/2)/(12n!*sqrt(Pi)) (suggested by WolframAlpha).
a(n) = +a(n-1) +4*a(n-2) -4*a(n-3) -6*a(n-4) +6*a(n-5) +4*a(n-6) -4*a(n-7) -a(n-8) +a(n-9). a(n) = (n+3)*(n+2)*(2*n^2+2*(-1)^n*n+10*n+5*(-1)^n+11)/96. [R. J. Mathar, Oct 23 2010]
MATHEMATICA
CoefficientList[Series[(1 + x + 4 x^2 + x^3 + x^4)/((1 - x)^5 (1 + x)^4), {x, 0, 36}], x] (* Michael De Vlieger, Jul 25 2023 *)
CROSSREFS
Sequence in context: A134861 A063610 A369650 * A047187 A048043 A370115
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Oct 22 2010
STATUS
approved

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Last modified March 29 10:22 EDT 2024. Contains 371268 sequences. (Running on oeis4.)