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Search: id:A046714
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| 1, 6, 32, 165, 839, 4237, 21317, 107014, 536500, 2687362, 13453606, 67326816, 336842092, 1684953360, 8427441240, 42146901045, 210769862895, 1053978959265, 5270372435025, 26353629438315, 131774711311995
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OFFSET
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0,2
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COMMENT
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i) Homogeneous recursion: a(n) = (3*(3*n+1)/(n+1))*a(n-1)-(10*(2*n-1)/(n+1))*a(n-2), a(-1) := 0, a(0)=1, n >= 1. ii) Hypergeometric 2F1 form: 2*a(n) = 5^(n+1)-binomial(2*(n+1), n+1)*hypergeom([ -n-1,1 ],[ 1/2 ],-1/4).
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FORMULA
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a(n) = sum(C(k)*5^(n-k), k=0..n), C(k)=A000108(k) (Catalan); a(n) = 5*a(n-1)+ C(n), a(0)=1; G.f.: c(x)/(1-5*x), where c(x) = g.f. for Catalan numbers A000108.
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CROSSREFS
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A000108, A000351.
Sequence in context: A083320 A097139 A034942 this_sequence A129171 A082585 A084326
Adjacent sequences: A046711 A046712 A046713 this_sequence A046715 A046716 A046717
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KEYWORD
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easy,nonn
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de)
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