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Search: id:A091520
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| A091520 |
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a(n) = 4^n(Sum_{i=0,n} binomial(2i,i)/(-4)^i). |
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+0
1
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| 1, 2, 14, 36, 214, 604, 3340, 9928, 52582, 161708, 831588, 2620920, 13187836, 42350744, 209519576, 682960784, 3332923526, 10998087884, 53067486836, 176924683544, 845545262996, 2843923177544, 13479791673896, 45685735967984
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OFFSET
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0,2
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FORMULA
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G.f.: 1/((1-4x)sqrt(1+4x)). na(n)=2a(n-1)+8(2n-1)a(n-2).
Asymptotics: a(n) ~ 4^n/sqrt(2).
G.f. y=A(x) satisfies (16x^2-1)y'+(24x+2)y=0 and y'^3+8y'^2*y^3+216y^5-256y^7=0.
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PROGRAM
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(PARI) a(n)=4^n*sum(i=0, n, binomial(2*i, i)/(-4)^i)
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CROSSREFS
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Sequence in context: A134647 A004117 A135706 this_sequence A108597 A062548 A067293
Adjacent sequences: A091517 A091518 A091519 this_sequence A091521 A091522 A091523
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KEYWORD
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nonn
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AUTHOR
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Michael Somos, Jan 18 2004
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