A022815 Number of terms in 5th derivative of a function composed with itself n times.

1, 7, 23, 55, 110, 196, 322, 498, 735, 1045, 1441, 1937, 2548, 3290, 4180, 5236, 6477, 7923, 9595, 11515, 13706, 16192, 18998, 22150, 25675, 29601, 33957, 38773, 44080, 49910, 56296, 63272, 70873, 79135, 88095, 97791, 108262, 119548, 131690

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Examples

			a(7) = 7*28 + (7*0+6*1+5*3+4*6+3*10+2*15+1*21) = 322. [_Bruno Berselli_, Jun 22 2013]
		

References

• W. C. Yang (yang(AT)math.wisc.edu), Derivatives of self-compositions of functions, preprint, 1997.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..10000
• W. C. Yang, Derivatives are essentially integer partitions, Discrete Mathematics, 222(1-3), July 2000, 235-245.

Crossrefs

Cf. A008778, A022811-A022818, A024207-A024210.

Programs

Magma

[n*(n+1)*(n^2+13*n-2)/24: n in [1..40]]; // Vincenzo Librandi, Oct 10 2011

Formula

a(n) = n*(n+1)*(n^2+13*n-2)/24. - John W. Layman, Apr 27 2000

G.f.: x*(1-2*x^2+2*x)/(1-x)^5. [Maksym Voznyy (voznyy(AT)mail.ru), Aug 11 2009]

a(n) = n*A000217(n) + sum((n-i)*A000217(i), i=0..n-1). [Bruno Berselli, Jun 23 2013]

Extensions

G.f. proposed by Maksym Voznyy checked and corrected by R. J. Mathar, Sep 16 2009.

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