A186271 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

A186271

a(n)=Product{k=0..n, A001333(k)}.

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: A376619 A052445 A351130 * A320949 A361056 A101389

Adjacent sequences: A186268 A186269 A186270 * A186272 A186273 A186274

KEYWORD

nonn,easy

AUTHOR

Paul Barry, Feb 16 2011

STATUS

approved