A215626 Number of terms in 8th derivative of a function composed with itself n times.

1, 22, 129, 468, 1309, 3101, 6539, 12644, 22857, 39148, 64141, 101256, 154869, 230491, 334967, 476696, 665873, 914754, 1237945, 1652716, 2179341, 2841465, 3666499, 4686044, 5936345, 7458776, 9300357, 11514304, 14160613, 17306679, 21027951, 25408624, 30542369

Offset: 1

Author

Alois P. Heinz, Aug 18 2012

Keywords

• nonn

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

Row n=8 of A022818.

Programs

Maple

a:= n-> n*(n+6)*(92+(-713+(722+(568+(50+n)*n)*n)*n)*n)/5040:
seq(a(n), n=1..40);

Mathematica

CoefficientList[Series[(x^6-7x^5+15x^4-4x^3-19x^2+14x+1)x/(x-1)^8,{x,0,40}],x]//Rest (* Harvey P. Dale, Aug 02 2020 *)

Formula

G.f.: (x^6-7*x^5+15*x^4-4*x^3-19*x^2+14*x+1)*x/(x-1)^8.

a(n) = n*(n+6)*(n^5+50*n^4+568*n^3+722*n^2-713*n+92)/5040.