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A102592
a(n) = Sum_{k=0..n} binomial(2n+1, 2k)*5^(n-k).
1
1, 8, 80, 832, 8704, 91136, 954368, 9994240, 104660992, 1096024064, 11477712896, 120196169728, 1258710630400, 13181388849152, 138037296103424, 1445545331654656, 15137947242201088, 158526641599938560
OFFSET
0,2
COMMENTS
In general, Sum_{k=0..n} binomial(2n+1,2k)*r^(n-k) has g.f. (1-(r-1)x)/(1-2(r+1)+(r-1)^2x^2) and a(n) = ((sqrt(r)-1)^(2n+1) + (sqrt(r)+1)^(2n+1))/(2*sqrt(r)).
FORMULA
G.f.:(1-4x)/(1-12x+16x^2);
a(n) = 12*a(n-1) - 16*a(n-2);
a(n) = sqrt(5)*(sqrt(5)-1)^(2n+1)/10 + sqrt(5)*(sqrt(5)+1)^(2n+1)/10.
a(n) = Sum_{k=0..n} binomial(2n+1, k+1)*5^k. - Paul Barry, May 27 2005
a(n) = 4^(n+1)*A001519(n+1). - N. J. A. Sloane, Apr 13 2011
a(n) = 5^n* 2F1(-n-1/2, -n ; 1/2 ; 1/5). - R. J. Mathar, Aug 23 2024
CROSSREFS
Sequence in context: A299871 A136949 A346178 * A345081 A320759 A233123
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Jan 22 2005
STATUS
approved