A132375 - OEIS

A132375

Expansion of c(8*x^2)/(1 - x*c(8*x^2)), where c(x) is the g.f. of A000108.

1, 1, 9, 17, 153, 353, 3177, 8113, 73017, 198401, 1785609, 5060433, 45543897, 133071009, 1197639081, 3581326065, 32231934585, 98156060225, 883404542025, 2730108129937, 24570973169433, 76862217117665, 691759954058985

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OFFSET

0,3

COMMENTS

Hankel transform is 8^C(n+1, 2).

Series reversion of x*(1+x)/(1+2*x+9*x^2).

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

FORMULA

a(n) = Sum_{k=0..n} A120730(n,k) * 8^(n-k).

From G. C. Greubel, Nov 08 2022: (Start)

a(n) = (9*(n+1)*a(n-1) + 32*(n-2)*a(n-2) - 288*(n-2)*a(n-3))/(n+1).

G.f.: (1 - sqrt(1-32*x^2))/(16*x^2 - x*(1 - sqrt(1-32*x^2))). (End)

MATHEMATICA

CoefficientList[Series[(1-Sqrt[1-32*x^2])/(16*x^2-x*(1-Sqrt[1-32*x^2])), {x, 0, 40}], x] (* G. C. Greubel, Nov 08 2022 *)

PROG

(Magma) R<x>:=PowerSeriesRing(Rationals(), 40); Coefficients(R!( (1-Sqrt(1-32*x^2))/(16*x^2 -x*(1-Sqrt(1-32*x^2))) )); // G. C. Greubel, Nov 08 2022

(SageMath)

def A120730(n, k): return 0 if (n>2*k) else binomial(n, k)*(2*k-n+1)/(k+1)

def A132375(n): return sum(8^(n-k)*A120730(n, k) for k in range(n+1))

[A132375(n) for n in range(51)] # G. C. Greubel, Nov 08 2022

CROSSREFS

Cf. A001405, A126087, A128386, A121724, A128387, A121725.

Sequence in context: A177166 A073221 A110462 * A110360 A371031 A123836

Adjacent sequences: A132372 A132373 A132374 * A132376 A132377 A132378

KEYWORD

easy,nonn

AUTHOR

Philippe Deléham, Nov 10 2007

STATUS

approved