The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A022815 Number of terms in 5th derivative of a function composed with itself n times. 5
 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 (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 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. 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] EXAMPLE a(7) = 7*28 + (7*0+6*1+5*3+4*6+3*10+2*15+1*21) = 322. [Bruno Berselli, Jun 22 2013] PROG (Magma) [n*(n+1)*(n^2+13*n-2)/24: n in [1..40]]; // Vincenzo Librandi, Oct 10 2011 CROSSREFS Cf. A008778, A022811-A022818, A024207-A024210. Sequence in context: A211791 A004068 A261893 * A172252 A027116 A151718 Adjacent sequences: A022812 A022813 A022814 * A022816 A022817 A022818 KEYWORD nonn,easy AUTHOR N. J. A. Sloane. 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. STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified June 1 11:52 EDT 2023. Contains 363068 sequences. (Running on oeis4.)