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A099929
Central Pellonomial coefficients.
4
1, 2, 30, 2436, 1166438, 3248730940, 52755584809356, 4992850354675749192, 2754130291777980970686150, 8854642279944231931659815098860, 165923943638796574201560736475319416580, 18121679707218614746613513717704194807763644600
OFFSET
0,2
LINKS
FORMULA
a(n) = A099927(2n, n).
a(n) ~ (1+sqrt(2))^(n^2) / c, where c = A256831 = 1.141982569667791206028... . - Vaclav Kotesovec, Apr 10 2015
MAPLE
p:= proc(n) p(n):= `if`(n<2, n, 2*p(n-1)+p(n-2)) end:
f:= proc(n) f(n):= `if`(n=0, 1, p(n)*f(n-1)) end:
a:= n-> f(2*n)/f(n)^2:
seq(a(n), n=0..15); # Alois P. Heinz, Aug 15 2013
MATHEMATICA
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 *)
PROG
(Sage)
P=[lucas_number1(n, 2, -1) for n in [0..30]]
[prod(P[1:2*n+1])/(prod(P[1:n+1]))^2 for n in [0..14]] # Tom Edgar, Apr 10 2015
CROSSREFS
KEYWORD
nonn
AUTHOR
Ralf Stephan, Nov 03 2004
STATUS
approved