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A121545
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Coefficients of Taylor series expansion of the operad Prim L.
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1
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0, 1, 1, 4, 17, 81, 412, 2192, 12049, 67891, 390041, 2276176, 13455356, 80402284, 484865032, 2947107384, 18036248337, 111046920567, 687345582787, 4274642610932, 26697307240777, 167377288848977
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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REFERENCES
| Philippe Leroux, An equivalence of categories motivated by weighted directed graphs, arXiv:math-ph/0709.3453.
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LINKS
| Olivier Gerard, Table of n, a(n) for n = 0..50
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FORMULA
| G.f.: sin^2( (1/3)*arcsin(sqrt(27*x/4)) ) / ( 3/4 + sin^2( (1/3)*arcsin(sqrt(27*x/4)) )).
As to a signed variant for n>0: (1, -1, 4, -17,...), a(n) = upper left term of M^n, M = the following infinite square production matrix:
1, 1, 0, 0, 0, 0,...
-2, -2, 1, 0, 0, 0,...
3, 3, -2, 1, 0, 0,...
-4, -4, 3, -2, 1, 0,...
5, 5, -4, 3, -2, 1,...
-6, -6, 5, -4, 3, -2,...
...
(each column is (1, -2, 3, -4, 5,...) prepended with (0, 0, 1, 2, 3,...) zeros by columns).
- Gary W. Adamson, Jul 13 2011
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CROSSREFS
| Cf. A006013.
Sequence in context: A204326 A151250 A174810 * A078845 A181517 A110771
Adjacent sequences: A121542 A121543 A121544 * A121546 A121547 A121548
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Oct 07 2007
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EXTENSIONS
| More terms from Olivier Gerard (olivier.gerard(AT)gmail.com), Oct 11 2007
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