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

1,2

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