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Search: id:A102592
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| A102592 |
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a(n)=sum k=0..n, C(2n+1,2k)5^(n-k). |
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+0
2
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| 1, 8, 80, 832, 8704, 91136, 954368, 9994240, 104660992, 1096024064, 11477712896, 120196169728, 1258710630400, 13181388849152, 138037296103424, 1445545331654656, 15137947242201088, 158526641599938560
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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In general, sum{k=0..n, C(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))/(2sqrt(r)).
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FORMULA
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G.f.:(1-4x)/(1-12x+16x^2); a(n)=12a(n-1)-16a(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, C(2n+1, k+1)5^k}; - Paul Barry (pbarry(AT)wit.ie), May 27 2005
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CROSSREFS
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Cf. A066443, A102591.
Sequence in context: A024101 A155144 A136949 this_sequence A053175 A051580 A060375
Adjacent sequences: A102589 A102590 A102591 this_sequence A102593 A102594 A102595
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Jan 22 2005
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