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

1, 1, 2, 4, 11, 32, 112, 415, 1732, 7678, 37115, 190016, 1039546, 5996083, 36528196, 233492044, 1564012751, 10940385668, 79762304116, 604791685063, 4760047233424, 38825234812882, 327641201731475, 2856835856307428, 25702896025566886, 238331921722835203

Offset: 0

Author

Vladeta Jovovic, Jan 19 2006

Keywords

• easy
• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..500

Crossrefs

Cf. A003724, A115276, A000246, A102736, A088009, A001590.

Programs

Maple

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
# second Maple program:
a:= proc(n) option remember; `if`(n=0, 1, add(`if`(
      irem(j, 3)=0, 0, binomial(n-1, j-1)*a(n-j)), j=1..n))
    end:
seq(a(n), n=0..30);  # Alois P. Heinz, Mar 17 2015

Mathematica

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 *)

Formula

E.g.f.: exp(B(x)), where B(x) is e.g.f. of A011655.

Extensions

More terms from R. J. Mathar, Feb 06 2008