%I #18 Sep 08 2022 08:44:46

%S 1,7,23,55,110,196,322,498,735,1045,1441,1937,2548,3290,4180,5236,

%T 6477,7923,9595,11515,13706,16192,18998,22150,25675,29601,33957,38773,

%U 44080,49910,56296,63272,70873,79135,88095,97791,108262,119548,131690

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

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

%H Vincenzo Librandi, <a href="/A022815/b022815.txt">Table of n, a(n) for n = 1..10000</a>

%H 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 a(n) = n*(n+1)*(n^2+13*n-2)/24. - _John W. Layman_, Apr 27 2000

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

%F a(n) = n*A000217(n) + sum((n-i)*A000217(i), i=0..n-1). [_Bruno Berselli_, Jun 23 2013]

%e 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 (Magma) [n*(n+1)*(n^2+13*n-2)/24: n in [1..40]]; // _Vincenzo Librandi_, Oct 10 2011

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

%K nonn,easy

%O 1,2

%A _N. J. A. Sloane_.

%E G.f. proposed by Maksym Voznyy checked and corrected by _R. J. Mathar_, Sep 16 2009.

%E More terms from _Christian G. Bower_, Aug 15 1999.