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Search: id:A118181
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| A118181 |
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Row sums of triangle A118180: a(n) = Sum_{k=0..n} (3^k)^(n-k) for n>=0. |
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+0
3
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| 1, 2, 5, 20, 137, 1622, 33293, 1182440, 72811793, 7757988842, 1433154521621, 458101483131260, 253879024041595289, 243453910296759945662, 404765167247068325944349, 1164432505878183620543030480
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OFFSET
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0,2
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COMMENT
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Also equals column 0 of the matrix square of triangle A118180, where [A118180^2](n,k) = a(n-k)*(3^k)^(n-k) for n>=k>=0.
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FORMULA
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G.f.: A(x) = Sum_{n>=0} x^n/(1-3^n*x).
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EXAMPLE
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A(x) = 1/(1-x) + x/(1-3x) + x^2/(1-9x) + x^3/(1-27x) + ...
= 1 + 2*x + 5*x^2 + 20*x^3 + 137*x^4 + 1622*x^5 + 33293*x^6 +...
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MAPLE
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a(n)=sum(k=0, n, (3^k)^(n-k) )
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CROSSREFS
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Cf. A118180 (triangle), A118182 (antidiagonal sums); A118183, A118184.
Sequence in context: A156073 A006366 A012317 this_sequence A140988 A136650 A111885
Adjacent sequences: A118178 A118179 A118180 this_sequence A118182 A118183 A118184
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Apr 15 2006
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