A215627 Number of terms in 9th derivative of a function composed with itself n times.

1, 30, 210, 867, 2690, 6956, 15833, 32775, 63024, 114235, 197241, 326976, 523575, 813671, 1231910, 1822706, 2642259, 3760860, 5265508, 7262865, 9882576, 13280982, 17645255, 23197985, 30202250, 38967201, 49854195, 63283510, 79741677, 99789465, 124070556

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=9 of A022818.

Programs

Maple

a:= n-> n*(n+1)*(6000+(-30788+(29472+(13697+(1703+(75+n)*n)*n)*n)*n)*n)/40320:
seq(a(n), n=1..40);

Formula

G.f.: (5*x^6-28*x^5+53*x^4-27*x^3-24*x^2+21*x+1)*x/(1-x)^9.

a(n) = n*(n+1)*(n^6+75*n^5+1703*n^4+13697*n^3+29472*n^2-30788*n+6000)/40320.