A127945 Hankel transform of central coefficients of (1+k*x-2x^2)^n, k arbitrary integer.

1, -4, -32, 512, 16384, -1048576, -134217728, 34359738368, 17592186044416, -18014398509481984, -36893488147419103232, 151115727451828646838272, 1237940039285380274899124224, -20282409603651670423947251286016

Offset: 0

Author

Paul Barry, Feb 08 2007

Keywords

• easy
• sign

Comments

Hankel transform of A098332. The Hankel transform of e.g.f. Bessel_I(0,2*sqrt(-2)x) and its k-th binomial transforms, are given by a(n). In general, the Hankel transform of e.g.f. Bessel_I(0,2*sqrt(m)x) and its binomial transforms is 2^n*m^C(n+1,2).

Unsigned version is A036442. - Philippe Deléham, Dec 11 2008

Links

• G. C. Greubel, Table of n, a(n) for n = 0..79

Crossrefs

Cf. A036442, A098332.

Programs

Magma

[2^n*(-2)^Binomial(n+1,2): n in [0..25]]; // G. C. Greubel, May 01 2018

Mathematica

Table[2^n*(-2)^Binomial[n+1,2], {n, 0, 25}] (* G. C. Greubel, May 01 2018 *)

PARI

for(n=0,25, print1(2^n*(-2)^binomial(n+1,2), ", ")) \\ G. C. Greubel, May 01 2018

Formula

a(n) = (cos(Pi*n/2) - sin(Pi*n/2))*4^n*2^C(n,2).

a(n) = 2^n*(-2)^C(n+1,2).