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A186271 a(n)=Product{k=0..n, A001333(k)}. 0
1, 1, 3, 21, 357, 14637, 1449063, 346326057, 199830134889, 278363377900377, 936136039878967851, 7600488507777339982269, 148977175240943640992454669, 7049748909576694035403947391749, 805384464676770256686653161875581007 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

a(n) is the determinant of the symmetric matrix (if(j<=floor((i+j)/2), Pell(j+1),

Pell(i+1)))_{0<=i,j<=n}, where Pell(n)=A000129(n).

LINKS

Table of n, a(n) for n=0..14.

FORMULA

a(n)=Product{k=0..n, sum{j=0..floor(k/2), binomial(k,2j)*2^j}}.

a(n) ~ c * (1+sqrt(2))^(n*(n+1)/2) / 2^(n+1), where c = 1.6982679851338713863950411843311686297311132648098280324748781109134... . - Vaclav Kotesovec, Jul 11 2015

EXAMPLE

a(3)=21 since det[1, 1, 1, 1; 1, 2, 2, 2; 1, 2, 5, 5; 1, 2, 5, 12]=21.

MATHEMATICA

Table[Product[Sum[Binomial[k, 2*j]*2^j, {j, 0, Floor[k/2]}], {k, 0, n}], {n, 0, 15}] (* Vaclav Kotesovec, Jul 11 2015 *)

Table[FullSimplify[Product[((1+Sqrt[2])^k + (1-Sqrt[2])^k)/2, {k, 0, n}]], {n, 0, 15}] (* Vaclav Kotesovec, Jul 11 2015 *)

CROSSREFS

Cf. A186269.

Sequence in context: A332928 A083228 A052445 * A320949 A101389 A108716

Adjacent sequences:  A186268 A186269 A186270 * A186272 A186273 A186274

KEYWORD

nonn,easy

AUTHOR

Paul Barry, Feb 16 2011

STATUS

approved

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Last modified September 22 17:39 EDT 2021. Contains 347607 sequences. (Running on oeis4.)