A022817 Number of terms in 7th derivative of a function composed with itself n times.

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

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

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.

Crossrefs

Cf. A008778, A022811-A022816, A024207-A024210.

Row n=4 of A022818.

Programs

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 *)

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

Extensions

More terms from Christian G. Bower, Aug 15 1999.