A141532 Inverse binomial transform of A141425.

1, 1, 1, -2, 4, -8, 7, 22, -125, 376, -878, 1756, -3143, 5188, -8189, 13102, -22928, 45856, -101549, 232618, -524285, 1137148, -2362874, 4725748, -9185771, 17574376, -33554429, 64717378, -127043276, 254086552, -515347553, 1052218462, -2147483645

Offset: 0

Author

Paul Curtz, Aug 12 2008

Keywords

• sign

Comments

This is the inverse binomial transform of A141425 if interpreted with offset 0.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (-6,-15,-20,-15,-6).

Crossrefs

Cf. A000748, A049347.

Programs

Magma

I:=[1,1,-2,4,-8]; [1] cat [n le 5 select I[n] else -6*Self(n-1) -15*Self(n-2) -20*Self(n-3) -15*Self(n-4) -6*Self(n-5): n in [1..40]]; // G. C. Greubel, Mar 30 2021

Mathematica

LinearRecurrence[{-6,-15,-20,-15,-6}, {1,1,1,-2,4,-8}, 40] (* G. C. Greubel, Mar 30 2021 *)

Sage

def A141532_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1 +7*x +22*x^2 +39*x^3 +42*x^4 +27*x^5)/((1+x+x^2)*(1+3*x+3*x^2)*(1+2*x)) ).list()
A141532_list(40) # G. C. Greubel, Mar 30 2021

Formula

G.f.: (1 +7*x +22*x^2 +39*x^3 +42*x^4 +27*x^5)/((1+x+x^2)*(1+3*x+3*x^2)*(1+2*x)). - R. J. Mathar, Nov 11 2008

From G. C. Greubel, Mar 30 2021: (Start)

a(n) = (9/2)*[n=0] + (-2)^(n-1) - (3/2)*( ChebyshevU(n, -1/2) + 2*ChebyshevU(n-1, -1/2) + 3^((n-1)/2)*(sqrt(3)*ChebyshevU(n, -sqrt(3)/2) + 2*ChebyshevU(n-1, -sqrt(3)/2)) ).

a(n) = (9/2)*[n=0] + (-2)^(n-1) - (3/2)*(A049347(n) + 2*A049347(n-1) + A000748(n) + 2*A000748(n-1) ). (End)

Extensions

Extended by R. J. Mathar, Nov 11 2008