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A022817
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Number of terms in 7th derivative of a function composed with itself n times.
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8
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1, 15, 74, 237, 599, 1301, 2541, 4586, 7785, 12583, 19536, 29327, 42783, 60893, 84827, 115956, 155873, 206415, 269686, 348081, 444311, 561429, 702857, 872414, 1074345, 1313351, 1594620, 1923859, 2307327, 2751869, 3264951, 3854696, 4529921, 5300175, 6175778
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OFFSET
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1,2
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REFERENCES
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W. C. Yang (yang(AT)math.wisc.edu), Derivatives of self-compositions of functions, preprint, 1997.
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LINKS
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FORMULA
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a(n) = n/720 * (n^5 + 39*n^4 + 355*n^3 + 645*n^2 - 356*n + 36).
G.f.: (x^5-4*x^4+x^3+10*x^2-8*x-1)*x/(x-1)^7. - Alois P. Heinz, Aug 18 2012
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MAPLE
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a:= n-> n*(36+(-356+(645+(355+(39+n)*n)*n)*n)*n)/720:
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MATHEMATICA
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Table[(n/720*(n^5+39*n^4+355*n^3+645*n^2-356*n+36)), {n, 1, 100}] (* Vincenzo Librandi, Aug 18 2012 *)
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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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