cp's OEIS Frontend

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

%I A022815 #20 Jul 08 2025 17:10:33
%S A022815 1,7,23,55,110,196,322,498,735,1045,1441,1937,2548,3290,4180,5236,
%T A022815 6477,7923,9595,11515,13706,16192,18998,22150,25675,29601,33957,38773,
%U A022815 44080,49910,56296,63272,70873,79135,88095,97791,108262,119548,131690
%N A022815 Number of terms in 5th derivative of a function composed with itself n times.
%D A022815 W. C. Yang (yang(AT)math.wisc.edu), Derivatives of self-compositions of functions, preprint, 1997.
%H A022815 Vincenzo Librandi, <a href="/A022815/b022815.txt">Table of n, a(n) for n = 1..10000</a>
%H A022815 W. C. Yang, <a href="http://dx.doi.org/10.1016/S0012-365X(99)00412-4">Derivatives are essentially integer partitions</a>, Discrete Mathematics, 222(1-3), July 2000, 235-245.
%F A022815 a(n) = n*(n+1)*(n^2+13*n-2)/24. - _John W. Layman_, Apr 27 2000
%F A022815 G.f.: x*(1-2*x^2+2*x)/(1-x)^5. [Maksym Voznyy (voznyy(AT)mail.ru), Aug 11 2009]
%F A022815 a(n) = n*A000217(n) + sum((n-i)*A000217(i), i=0..n-1). [_Bruno Berselli_, Jun 23 2013]
%e A022815 a(7) = 7*28 + (7*0+6*1+5*3+4*6+3*10+2*15+1*21) = 322. [_Bruno Berselli_, Jun 22 2013]
%o A022815 (Magma) [n*(n+1)*(n^2+13*n-2)/24: n in [1..40]]; // _Vincenzo Librandi_, Oct 10 2011
%Y A022815 Cf. A008778, A022811-A022818, A024207-A024210.
%K A022815 nonn,easy
%O A022815 1,2
%A A022815 _N. J. A. Sloane_
%E A022815 G.f. proposed by Maksym Voznyy checked and corrected by _R. J. Mathar_, Sep 16 2009.
%E A022815 More terms from _Christian G. Bower_, Aug 15 1999.