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 A022817 Number of terms in 7th derivative of a function composed with itself n times. 8
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 REFERENCES W. C. Yang (yang(AT)math.wisc.edu), Derivatives of self-compositions of functions, preprint, 1997. LINKS Alois P. Heinz, Table of n, a(n) for n = 1..1000 W. C. Yang, Derivatives are essentially integer partitions, Discrete Mathematics, 222(1-3), July 2000, 235-245. FORMULA 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 MAPLE a:= n-> n*(36+(-356+(645+(355+(39+n)*n)*n)*n)*n)/720: seq(a(n), n=1..40); # Alois P. Heinz, Aug 18 2012 MATHEMATICA 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 *) CROSSREFS Cf. A008778, A022811-A022816, A024207-A024210. Row n=4 of A022818. Sequence in context: A002603 A212562 A212092 * A171341 A080841 A022675 Adjacent sequences: A022814 A022815 A022816 * A022818 A022819 A022820 KEYWORD nonn AUTHOR N. J. A. Sloane. EXTENSIONS More terms from Christian G. Bower, Aug 15 1999. STATUS approved

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