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A099929 Central Pellonomial coefficients. 4

%I

%S 1,2,30,2436,1166438,3248730940,52755584809356,4992850354675749192,

%T 2754130291777980970686150,8854642279944231931659815098860,

%U 165923943638796574201560736475319416580,18121679707218614746613513717704194807763644600

%N Central Pellonomial coefficients.

%H Alois P. Heinz, <a href="/A099929/b099929.txt">Table of n, a(n) for n = 0..50</a>

%F a(n) = A099927(2n, n).

%F a(n) ~ (1+sqrt(2))^(n^2) / c, where c = A256831 = 1.141982569667791206028... . - _Vaclav Kotesovec_, Apr 10 2015

%p p:= proc(n) p(n):= `if`(n<2, n, 2*p(n-1)+p(n-2)) end:

%p f:= proc(n) f(n):= `if`(n=0, 1, p(n)*f(n-1)) end:

%p a:= n-> f(2*n)/f(n)^2:

%p seq(a(n), n=0..15); # _Alois P. Heinz_, Aug 15 2013

%t Pell[m_]:=Expand[((1+Sqrt[2])^m-(1-Sqrt[2])^m)/(2*Sqrt[2])]; Table[Product[Pell[k],{k,1,2*n}]/(Product[Pell[k],{k,1,n}])^2,{n,0,20}] (* _Vaclav Kotesovec_, Apr 10 2015 *)

%o (Sage)

%o P=[lucas_number1(n, 2, -1) for n in [0..30]]

%o [prod(P[1:2*n+1])/(prod(P[1:n+1]))^2 for n in [0..14]] # _Tom Edgar_, Apr 10 2015

%Y Cf. A000129, A099927, A256831.

%K nonn

%O 0,2

%A _Ralf Stephan_, Nov 03 2004

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Last modified August 11 08:17 EDT 2022. Contains 356055 sequences. (Running on oeis4.)