login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A304797 Expansion of x * (d/dx) Sum_{k>=0} k!*x^(k*(k+1)/2)/Product_{j=1..k} (1 - x^j). 1
0, 1, 2, 9, 12, 25, 66, 91, 152, 243, 570, 715, 1212, 1729, 2702, 5265, 6960, 10489, 15318, 22363, 31100, 57771, 72534, 109411, 151032, 219025, 293930, 421281, 680820, 883369, 1256010, 1727971, 2396000, 3235419, 4447506, 5894875, 9266580, 11691001, 16380470, 21774753 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Sum of all parts of all compositions (ordered partitions) of n into distinct parts.

LINKS

Table of n, a(n) for n=0..39.

Index entries for sequences related to compositions

FORMULA

a(n) = n*A032020(n).

MAPLE

b:= proc(n, k) option remember; `if`(k<0 or n<0, 0,

     `if`(k=0, `if`(n=0, 1, 0), b(n-k, k) +k*b(n-k, k-1)))

    end:

a:= n-> n*add(b(n, k), k=0..floor((sqrt(8*n+1)-1)/2)):

seq(a(n), n=0..50);  # Alois P. Heinz, May 18 2018

MATHEMATICA

nmax = 39; CoefficientList[Series[x D[Sum[k! x^(k (k + 1)/2)/Product[1 - x^j, {j, 1, k}], {k, 0, nmax}], x], {x, 0, nmax}], x]

CROSSREFS

Cf. A001787, A032020, A066186, A066189, A097910, A303664.

Sequence in context: A053900 A318681 A183207 * A178312 A253608 A126977

Adjacent sequences:  A304794 A304795 A304796 * A304798 A304799 A304800

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, May 18 2018

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 23 14:54 EDT 2019. Contains 328345 sequences. (Running on oeis4.)