A127947 - OEIS

%I #12 Sep 08 2022 08:45:29

%S 1,10,500,125000,156250000,976562500000,30517578125000000,

%T 4768371582031250000000,3725290298461914062500000000,

%U 14551915228366851806640625000000000

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

%C 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).

%H G. C. Greubel, <a href="/A127947/b127947.txt">Table of n, a(n) for n = 0..52</a>

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

%t Table[2^n*5^Binomial[n+1,2], {n,0,30}] (* _G. C. Greubel_, May 03 2018 *)

%o (PARI) for(n=0, 30, print1(2^n*5^binomial(n+1,2), ", ")) \\ _G. C. Greubel_, May 03 2018

%o (Magma) [2^n*5^Binomial(n+1,2): n in [0..30]]; // _G. C. Greubel_, May 03 2018

%K easy,nonn

%O 0,2

%A _Paul Barry_, Feb 08 2007