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A113774 Number of partitions of {1,...,n} into block sizes not a multiple of 3.

%I A113774 #16 Aug 09 2015 00:30:41
%S A113774 1,1,2,4,11,32,112,415,1732,7678,37115,190016,1039546,5996083,
%T A113774 36528196,233492044,1564012751,10940385668,79762304116,604791685063,
%U A113774 4760047233424,38825234812882,327641201731475,2856835856307428,25702896025566886,238331921722835203
%N A113774 Number of partitions of {1,...,n} into block sizes not a multiple of 3.
%H A113774 Alois P. Heinz, <a href="/A113774/b113774.txt">Table of n, a(n) for n = 0..500</a>
%F A113774 E.g.f.: exp(B(x)), where B(x) is e.g.f. of A011655.
%p A113774 nmax := 30: B := add(op(1+(i mod 3),[0,1,1])*x^i/i!,i=0..nmax) : egf := 0 : for i from 0 to nmax do egf := convert(egf+taylor(B^i,x=0,nmax+1)/i!,polynom) : od: for i from 0 to nmax do printf("%d ", i!*coeftayl(egf,x=0,i)) ; od: # _R. J. Mathar_, Feb 06 2008
%p A113774 # second Maple program:
%p A113774 a:= proc(n) option remember; `if`(n=0, 1, add(`if`(
%p A113774       irem(j, 3)=0, 0, binomial(n-1, j-1)*a(n-j)), j=1..n))
%p A113774     end:
%p A113774 seq(a(n), n=0..30);  # _Alois P. Heinz_, Mar 17 2015
%t A113774 a=Sum[x^(3i)/(3i)!,{i,1,20}]; Range[0, 20]! CoefficientList[Series[Exp[Exp[x] - 1 - a], {x, 0, 20}], x] (* _Geoffrey Critzer_, Jan 02 2011 *)
%Y A113774 Cf. A003724, A115276, A000246, A102736, A088009, A001590.
%K A113774 easy,nonn
%O A113774 0,3
%A A113774 _Vladeta Jovovic_, Jan 19 2006
%E A113774 More terms from _R. J. Mathar_, Feb 06 2008