A127947 Hankel transform of central coefficients of (1+k*x+5x^2)^n, k arbitrary integer.

1, 10, 500, 125000, 156250000, 976562500000, 30517578125000000, 4768371582031250000000, 3725290298461914062500000000, 14551915228366851806640625000000000

Offset

0,2

Comments

Hankel transform of A098264. The Hankel transform of e.g.f. Bessel_I(0,2*sqrt(5)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).

Links

G. C. Greubel, Table of n, a(n) for n = 0..52

Formula

a(n) = 2^n*5^C(n+1,2).

Mathematica

Table[2^n*5^Binomial[n+1, 2], {n, 0, 30}] (* G. C. Greubel, May 03 2018 *)

Prog

(PARI) for(n=0, 30, print1(2^n*5^binomial(n+1, 2), ", ")) \\ G. C. Greubel, May 03 2018
(Magma) [2^n*5^Binomial(n+1, 2): n in [0..30]]; // G. C. Greubel, May 03 2018

Crossrefs

Sequence in context: A071096 A039835 A293090 * A095232 A042209 A272394

Adjacent sequences: A127944 A127945 A127946 * A127948 A127949 A127950

Keyword

easy,nonn

Author

Paul Barry, Feb 08 2007

Status

approved