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A113775 Number of sets of lists (cf. A000262) whose list sizes are not a multiple of 3. 1
1, 1, 3, 7, 49, 321, 2131, 19783, 195777, 2101249, 25721731, 340358151, 4902173233, 75688032577, 1253701725459, 22347046050631, 418439924732161, 8318748086461953, 175769214730290307, 3871849719998940679, 89734800330818444721, 2187944831367633226561 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..445

FORMULA

E.g.f.: exp(x*(1+x)/(1-x^3)).

a(n) = a(n-1) + 2*(n-1)*a(n-2) + 2*(n-3)*(n-2)*(n-1)*a(n-3) + 2*(n-3)*(n-2)*(n-1)*a(n-4) + (n-4)*(n-3)*(n-2)*(n-1)*a(n-5) - (n-6)*(n-5)*(n-4)*(n-3)*(n-2)*(n-1)*a(n-6). - Vaclav Kotesovec, Sep 25 2013

a(n) ~ 6^(-1/4) * n^(n-1/4) * exp(2/3*sqrt(6*n)-n) * (1 - 43/(48*sqrt(6*n))). - Vaclav Kotesovec, Sep 25 2013

MAPLE

nmax := 30: B := x*(1+x)/(1-x^3) : 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`(0=

      irem(j, 3), 0, a(n-j)*j!*binomial(n-1, j-1)), j=1..n))

    end:

seq(a(n), n=0..25);  # Alois P. Heinz, May 10 2016

MATHEMATICA

CoefficientList[Series[E^(x*(1+x)/(1-x^3)), {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Sep 25 2013 *)

CROSSREFS

Cf. A000726, A003724, A115276, A000246, A102736, A088009, A001590.

Sequence in context: A275830 A190444 A118393 * A113236 A035499 A273092

Adjacent sequences:  A113772 A113773 A113774 * A113776 A113777 A113778

KEYWORD

easy,nonn

AUTHOR

Vladeta Jovovic, Jan 19 2006

EXTENSIONS

2 more terms from R. J. Mathar, Feb 06 2008

STATUS

approved

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Last modified December 6 03:18 EST 2016. Contains 278772 sequences.