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Search: id:A118396
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| A118396 |
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Eigenvector of triangle A118394; E.g.f.: exp( Sum_{n>=0} x^(3^n) ). |
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+0
3
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| 1, 1, 1, 7, 25, 61, 481, 2731, 10417, 454105, 4309921, 23452111, 592433161, 6789801877, 46254009985, 893881991731, 11548704851041, 93501748795441, 4828847934591937, 83867376656907415, 823025819684123641
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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E.g.f. of triangle A118394 is: exp(x+y*x^3), where A118394(n,k) = n!/k!/(n-3*k)!. More generally, given a triangle with e.g.f.: exp(x+y*x^b), the eigenvector will have e.g.f.: exp( Sum_{n>=0} x^(b^n) ).
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FORMULA
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a(n) = Sum_{k=0..[n/3]} n!/k!/(n-3*k)! *a(k) for n>=0, with a(0)=1.
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PROGRAM
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(PARI) {a(n)=n!*polcoeff(exp(sum(k=0, ceil(log(n+1)/log(3)), x^(3^k))+x*O(x^n)), n)}
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CROSSREFS
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Cf. A118394, A118395; variants: A118393, A118932.
Adjacent sequences: A118393 A118394 A118395 this_sequence A118397 A118398 A118399
Sequence in context: A098538 A033814 A118395 this_sequence A001845 A127765 A056685
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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), May 07 2006
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