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A173109
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Row sums of triangle A173108.
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4
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1, 1, 3, 6, 18, 58, 221, 935, 4361, 22082, 120336, 700652, 4333933, 28345089, 195233255, 1411303634, 10675375402, 84276173438, 692752181561, 5917018378495, 52416910416933, 480786834535246, 4559132648864256, 44632792689619592, 450518001943669545
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OFFSET
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0,3
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LINKS
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FORMULA
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G.f.: G(0)/(1-x^2)/(1+x) where G(k) = 1 - 2*x*(k+1)/((2*k+1)*(2*x*k-1) - x*(2*k+1)*(2*k+3)*(2*x*k-1)/(x*(2*k+3) - 2*(k+1)*(2*x*k+x-1)/G(k+1) )); (recursively defined continued fraction). - Sergei N. Gladkovskii, Jan 04 2013.
G.f.: ( G(0) - 1 )/(1-x^2) where G(k) = 1 + (1-x)/(1-x*k)/(1-x/(x+(1-x)/G(k+1) )); (recursively defined continued fraction). - Sergei N. Gladkovskii, Jan 22 2013
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EXAMPLE
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a(5) = 58 = 52 + 5 + 1.
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MAPLE
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b:= proc(n) option remember; `if`(n=0, 1,
add(b(n-j)*binomial(n-1, j-1), j=1..n))
end:
a:= n-> add(b(n-2*k), k=0..iquo(n, 2)):
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MATHEMATICA
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a[n_] := Sum[BellB[n-2k], {k, 0, Quotient[n, 2]}];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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