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

0,3

Links

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

Formula

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

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 *)

Crossrefs

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

Sequence in context: A268322 A148171 A318644 * A124504 A056324 A056325

Adjacent sequences: A113771 A113772 A113773 * A113775 A113776 A113777

Keyword

easy,nonn

Author

Vladeta Jovovic, Jan 19 2006

Extensions

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

Status

approved