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A084137 Binomial transform of A084136. 1
1, 2, 8, 32, 144, 672, 3200, 15360, 73984, 356864, 1722368, 8314880, 40144896, 193830912, 935886848, 4518838272, 21818834944, 105350561792, 508677324800, 2456111022080, 11859152338944, 57261051346944, 276480810549248 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Exponential self-convolution of companion Pell numbers (A002203), divided by 4. - Vladimir Reshetnikov, Oct 07 2016

LINKS

Table of n, a(n) for n=0..22.

FORMULA

G.f.: (1-4x)/((1-2x)(1-4x-4x^2)).

E.g.f.: exp(2x)cosh(sqrt(2)x)^2=(exp(x)cosh(sqrt(2)x))^2.

a(n) = (2+sqrt(8))^n/4+(2-sqrt(8))^n/4+2^n/2.

a(n) = (A084128(n)+2^n)/2.

a(n) = 2^(n-2)*(2 + A002203(n)). - Vladimir Reshetnikov, Oct 07 2016

MATHEMATICA

Table[2^(n-2) (2 + LucasL[n, 2]), {n, 0, 20}] (* Vladimir Reshetnikov, Oct 07 2016 *)

PROG

(PARI) a(n)=if(n<0, 0, polsym(4+4*x-x^2, n)[n+1]/4+2^(n-1))

CROSSREFS

Sequence in context: A150861 A150862 A150863 * A129400 A003304 A150864

Adjacent sequences:  A084134 A084135 A084136 * A084138 A084139 A084140

KEYWORD

easy,nonn

AUTHOR

Paul Barry, May 16 2003

STATUS

approved

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Last modified October 21 22:47 EDT 2019. Contains 328315 sequences. (Running on oeis4.)