A115944 Number of partitions of n into distinct factorials.

1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset

0

Comments

a(A115944(n)) > 0; a(A115944(n)) = 0;

a(A115647(n)) > 0;

what is the smallest n such that a(n) > 1?.

No such n exists as 0 <= a(n) <= 1, cf. formula;

a(A059590(n)) = 1. - Reinhard Zumkeller, Dec 04 2011

Links

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Index entries for sequences related to factorial numbers

Formula

G.f.: Product_{j>=1} (1 + x^(j!)). - Emeric Deutsch, Apr 06 2006

a(n! + k) = a(k) for k: 0 <= k < (n-1)! and a(n! + k)=0 for k: (n-1)! <= k < n!.

a(n! + k) = 0 for k: (n-1)! <= k < n!.

Example

a(32)=1 because we have [24,6,2].

Maple

g:=product(1+x^(j!), j=1..7): gser:=series(g, x=0, 125): seq(coeff(gser, x, n), n=1..122); # Emeric Deutsch, Apr 06 2006

Mathematica

max = 7; f[x_] := Product[ 1+x^(j!), {j, 1, max}]; A115944 = Take[ CoefficientList[ Series[ f[x], {x, 0, max!}], x], 106] (* Jean-François Alcover, Dec 28 2011, after Emeric Deutsch *)

Prog

(Haskell)
a115944 = p (tail a000142_list) where
   p _      0             = 1
   p (f:fs) m | m < f     = 0
              | otherwise = p fs (m - f) + p fs m
-- Reinhard Zumkeller, Dec 04 2011

Crossrefs

Cf. A064986.

Cf. A197183.

Sequence in context: A285498 A285504 A130093 * A166446 A103368 A055132

Adjacent sequences: A115941 A115942 A115943 * A115945 A115946 A115947

Keyword

nonn

Author

Reinhard Zumkeller, Feb 02 2006

Extensions

Offset changed and initial a(0)=1 added by Reinhard Zumkeller, Dec 04 2011

Status

approved