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A309538 Total number of factorial parts in all compositions of n. 1
0, 1, 3, 7, 17, 40, 93, 210, 469, 1036, 2268, 4928, 10640, 22848, 48832, 103936, 220416, 465920, 982016, 2064384, 4329472, 9060352, 18923520, 39452672, 82116609, 170655746, 354156549, 734003212, 1519386652, 3141533760, 6488588432, 13388218688, 27598521024 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..3312

FORMULA

G.f.: Sum_{k>=1} x^(k!)*(1-x)^2/(1-2*x)^2.

a(n) ~ c * 2^n * n, where c = 0.1914062649011611938476562500000000001880790961... - Vaclav Kotesovec, Aug 18 2019

MAPLE

g:= proc(n) local i; 1; for i from 2 do

      if n=% then 1; break elif n<% then 0; break fi;

      %*i od; g(n):=%

    end:

a:= proc(n) option remember; add(a(n-j)+

      `if`(g(j)=1, ceil(2^(n-j-1)), 0), j=1..n)

    end:

seq(a(n), n=0..33);

CROSSREFS

Cf. A000142, A102291.

Sequence in context: A147142 A298371 A106472 * A036885 A247300 A137682

Adjacent sequences:  A309535 A309536 A309537 * A309539 A309540 A309541

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Aug 06 2019

STATUS

approved

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Last modified April 21 10:28 EDT 2021. Contains 343149 sequences. (Running on oeis4.)