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A107233 An inverse Chebyshev transform of n^3. 1
0, 1, 8, 30, 96, 270, 720, 1820, 4480, 10710, 25200, 58212, 133056, 300300, 672672, 1492920, 3294720, 7220070, 15752880, 34179860, 73902400, 159074916, 341429088, 730122120, 1557593856, 3312591100, 7030805600, 14883258600, 31451414400 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Image of n^3 under the mapping of g(x)->(1/sqrt(1-4x^2))g(xc(x^2)) where c(x) is the g.f. of A000108.

LINKS

Table of n, a(n) for n=0..28.

FORMULA

G.f.: 4x(sqrt(1-4x^2)-1)^2(4x+1)/(sqrt(1-4x^2)(sqrt(1-4x^2)+2x-1)^4); a(n)=sum{k=0..floor(n/2), binomial(n, k)(n-2k)^3};

Conjecture: (n-1)*a(n)+4*(n-4)*a(n-1) -4*(n+4)*a(n-2) +16*(2-n)*a(n-3)=0. - R. J. Mathar, Nov 09 2012

From Vaclav Kotesovec, Nov 04 2017: (Start)

G.f.: x*(1 + 4*x) / ((1 - 2*x)^(5/2) * sqrt(1 + 2*x)).

a(n) ~ 2^(n + 1/2) * n^(3/2) / sqrt(Pi). (End)

MATHEMATICA

CoefficientList[Series[x*(1 + 4*x) / ((1 - 2*x)^(5/2) * Sqrt[1 + 2*x]), {x, 0, 30}], x] (* Vaclav Kotesovec, Nov 04 2017 *)

CROSSREFS

Cf. A100071, A001787.

Sequence in context: A232772 A213776 A113751 * A098213 A163613 A279217

Adjacent sequences:  A107230 A107231 A107232 * A107234 A107235 A107236

KEYWORD

easy,nonn

AUTHOR

Paul Barry, May 13 2005

STATUS

approved

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Last modified March 21 04:59 EDT 2019. Contains 321364 sequences. (Running on oeis4.)