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 A190444 E.g.f. exp(x+x^2+x^4) 0
 1, 1, 3, 7, 49, 201, 1411, 7183, 68097, 453169, 4523491, 34273911, 403454833, 3618761017, 45157828899, 445900023871, 6206361667201, 69111310499553, 1017103374816067, 12237616620289639, 195222691795726641, 2575612811875082281, 43240905591424459843, 608870179599833137647 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS FORMULA E.g.f. exp(x+x^2+x^4) a(n)=n!*sum(k=1..n, sum(j=floor((4*k-n)/3)..floor((4*k-n)/2), binomial(j,n-4*k+3*j)*binomial(k,j))/k!), n>0, a(0)=1. a(n) = a(n-1) + 2*(n-1)*a(n-2) + 4*(n-3)*(n-2)*(n-1)*a(n-4). - Vaclav Kotesovec, Oct 09 2013 a(n) ~ 2^(n/2-1) * n^(3*n/4) * exp(n^(1/4)/sqrt(2) - 3*n/4 + sqrt(n)/2 - 1/8) * (1 - 1/(4*sqrt(2)*n^(1/4)) + 43/(192*sqrt(n)) + 271/(768*sqrt(2)*n^(3/4))). - Vaclav Kotesovec, Oct 09 2013 MATHEMATICA CoefficientList[Series[E^(x+x^2+x^4), {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Oct 09 2013 *) PROG (Maxima) a(n):=n!*sum(sum(binomial(j, n-4*k+3*j)*binomial(k, j), j, floor((4*k-n)/3), floor((4*k-n)/2))/k!, k, 1, n); (PARI) N=33;  x='x+O('x^N); egf=exp(x+x^2+x^4); Vec(serlaplace(egf)) /* Joerg Arndt, Sep 15 2012 */ CROSSREFS Sequence in context: A327578 A062959 A275830 * A118393 A113775 A113236 Adjacent sequences:  A190441 A190442 A190443 * A190445 A190446 A190447 KEYWORD nonn AUTHOR Vladimir Kruchinin, May 24 2011 STATUS approved

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Last modified October 17 06:08 EDT 2019. Contains 328106 sequences. (Running on oeis4.)