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Search: id:A118186
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| A118186 |
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Row sums of triangle A118185: a(n) = Sum_{k=0..n} (4^k)^(n-k) for n>=0. |
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+0
3
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| 1, 2, 6, 34, 386, 8706, 395266, 35659778, 6476038146, 2336999211010, 1697654543745026, 2450521284684021762, 7120479243447937531906, 41112924905741324849774594, 477847273163370530909175414786
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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 A118185, where [A118185^2](n,k) = a(n-k)*(4^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/(1-4^n*x).
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EXAMPLE
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A(x) = 1/(1-x) + x/(1-4x) + x^2/(1-16x) + x^3/(1-64x) + ...
= 1 + 2*x + 6*x^2 + 34*x^3 + 386*x^4 + 8706*x^5 +...
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PROGRAM
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(PARI) a(n)=sum(k=0, n, (4^k)^(n-k) )
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CROSSREFS
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Cf. A118185 (triangle), A118187 (antidiagonal sums).
Sequence in context: A002685 A052878 A076863 this_sequence A075272 A101262 A135965
Adjacent sequences: A118183 A118184 A118185 this_sequence A118187 A118188 A118189
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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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