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 A113237 E.g.f.: exp(x*(1 - x^3 + x^4)/(1-x)). 2
 1, 1, 3, 13, 49, 381, 2971, 26713, 291873, 3262969, 41245651, 569262981, 8433896593, 136060620853, 2342471665899, 42987065380561, 838321137046081, 17272648375895793, 375413770580941603, 8579701021461918589, 205637099039964274161, 5158188565847339152621 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Number of partitions of {1,..,n} into any number of lists of size not equal to 4, where a list means an ordered subset, cf. A000262. LINKS Alois P. Heinz, Table of n, a(n) for n = 0..444 FORMULA Expression as a sum involving generalized Laguerre polynomials, in Mathematica notation: a(n)=n!*Sum[(-1)^k*LaguerreL[n - 4*k, -1, -1]/k!, {k, 0, Floor[n/4]}], n=0, 1.... Recurrence: a(n) = (2*n-1)*a(n-1) - (n-2)*(n-1)*a(n-2) - 4*(n-3)*(n-2)*(n-1)*a(n-4) + 8*(n-4)*(n-3)*(n-2)*(n-1)*a(n-5) - 4*(n-5)*(n-4)*(n-3)*(n-2)*(n-1)*a(n-6). - Vaclav Kotesovec, Jun 24 2013 a(n) ~ n^(n-1/4)*exp(-3/2+2*sqrt(n)-n)/sqrt(2) * (1 + 187/(48*sqrt(n))). - Vaclav Kotesovec, Jun 24 2013 MAPLE a:= proc(n) option remember; `if`(n=0, 1, add(       `if`(j=4, 0, a(n-j)*binomial(n-1, j-1)*j!), j=1..n))     end: seq(a(n), n=0..30);  # Alois P. Heinz, May 10 2016 MATHEMATICA f[n_] := n!*Sum[(-1)^k*LaguerreL[n - 4*k, -1, -1]/k!, {k, 0, Floor[n/4]}]; Table[ f[n], {n, 0, 19}] Range[0, 19]!* CoefficientList[ Series[ Exp[x*(1 - x^3 + x^4)/(1 - x)], {x, 0, 19}], x] (* Robert G. Wilson v, Oct 21 2005 *) CROSSREFS Cf. A000262, A052845, A097514, A113235, A113236. Sequence in context: A241775 A045908 A118589 * A284329 A259338 A196907 Adjacent sequences:  A113234 A113235 A113236 * A113238 A113239 A113240 KEYWORD nonn AUTHOR Karol A. Penson, Oct 19 2005 STATUS approved

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Last modified May 31 12:20 EDT 2020. Contains 334748 sequences. (Running on oeis4.)