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A113775 Number of sets of lists (cf. A000262) whose list sizes are not a multiple of 3. 2
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
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
Sequence in context: A190444 A118393 A362522 * A113236 A035499 A273092
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 March 29 04:59 EDT 2024. Contains 371264 sequences. (Running on oeis4.)