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

Author

Paul Barry, Feb 08 2007

Keywords

• easy
• nonn

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

Programs

Magma

[2^n*5^Binomial(n+1,2): n in [0..30]]; // G. C. Greubel, May 03 2018

Mathematica

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

PARI

for(n=0, 30, print1(2^n*5^binomial(n+1,2), ", ")) \\ G. C. Greubel, May 03 2018

Formula

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