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A204062 G.f.: exp( Sum_{n>=1} A002203(n)^2 * x^n/n ) where A002203 are the companion Pell numbers. 8
1, 4, 26, 148, 867, 5048, 29428, 171512, 999653, 5826396, 33958734, 197925996, 1153597255, 6723657520, 39188347880, 228406429744, 1331250230601, 7759094953844, 45223319492482, 263580822001028, 1536261612513707, 8953988853081192, 52187671505973468 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..500

Index entries for linear recurrences with constant coefficients, signature (4,10,4,-1).

FORMULA

G.f.: 1/((1+x)^2*(1-6*x+x^2)).

Self-convolution of A026933.

Self-convolution 4th power of A204061.

a(n) = Pell(n-1)^2 + a(n-2) where Pell(n) = A000129(n).

a(n) = (1/8)*(A001109(n+2)+(-1)^n*(n+2)). - Bruno Berselli, Jan 10 2012

EXAMPLE

G.f.: A(x) = 1 + 4*x + 26*x^2 + 148*x^3 + 867*x^4 + 5048*x^5 +...

where

log(A(x)) = 2^2*x + 6^2*x^2/2 + 14^2*x^3/3 + 34^2*x^4/4 + 82^2*x^5/5 + 198^2*x^6/6 + 478^2*x^7/7 +...+ A002203(n)^2*x^n/n +...

MATHEMATICA

LinearRecurrence[{4, 10, 4, -1}, {1, 4, 26, 148}, 30] (* Vincenzo Librandi, Feb 12 2012 *)

PROG

(PARI) {A002203(n)=polcoeff(2*x*(1+x)/(1-2*x-x^2+x*O(x^n)), n)}

{a(n)=polcoeff(exp(sum(k=1, n, A002203(k)^2*x^k/k)+x*O(x^n)), n)}

CROSSREFS

Cf. A026933, A204061, A002203, A000129, A212442.

Sequence in context: A325587 A223627 A144068 * A121767 A092167 A124544

Adjacent sequences:  A204059 A204060 A204061 * A204063 A204064 A204065

KEYWORD

nonn,easy

AUTHOR

Paul D. Hanna, Jan 10 2012

STATUS

approved

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Last modified September 23 03:40 EDT 2020. Contains 337291 sequences. (Running on oeis4.)