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 A115944 Number of partitions of n into distinct factorials. 17
 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 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

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Last modified December 7 01:51 EST 2022. Contains 358649 sequences. (Running on oeis4.)