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A115944 Number of partitions of n into distinct factorials. 6
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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: A185916 A285498 A285504 * A285403 A183918 A283437

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

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Last modified November 20 00:39 EST 2017. Contains 294957 sequences.