OFFSET
0,4
LINKS
Vladimir Kruchinin, D. V. Kruchinin, Composita and their properties, arXiv:1103.2582 [math.CO], 2011-2013.
FORMULA
E.g.f.: exp((1 + x - sqrt(1 - 2 x - 3x^2))/(2(1 + x))).
a(n) = (n-1)!*Sum_{k=1..n} ((Sum_{j=k..n} C(n,j)*C(2*j-k-1, j-1)*(-1)^(n-j))/(k-1)!), n > 0. - Vladimir Kruchinin, Sep 07 2010
a(n) ~ sqrt(2)*3^(n + 1/2)*n^(n-1)/(8*exp(n - 1/2)). - Vaclav Kotesovec, Sep 29 2013
From Benedict W. J. Irwin, May 27 2016: (Start)
Let y(0)=1, y(1)=1, y(2)=1/2, y(3)=7/6,
Let -3n*(1+n)*y(n) - (12+20n+8n^2)*y(n+1) - (25+24n+6n^2)*y(n+2)+(n+3)*(n+4)*y(n+4) = 0,
a(n) = n!*y(n).
(End)
MATHEMATICA
a[n_] := (n-1)!*Sum[ ((-1)^(n+k)*Binomial[n, k]* HypergeometricPFQ[ {k/2 + 1/2, k/2, k-n}, {k, k+1}, 4])/(k-1)!, {k, 1, n}]; a[0] = 1; Table[ a[n], {n, 0, 18}] (* Jean-François Alcover, Dec 20 2011, after Vladimir Kruchinin *)
PROG
(Maxima) a(n):=(n-1)!*sum(sum(binomial(n, j)*binomial(2*j-k-1, j-1)*(-1)^(n-j), j, k, n)/(k-1)!, k, 1, n); /* Vladimir Kruchinin, Sep 07 2010 */
CROSSREFS
KEYWORD
easy,nice,nonn
AUTHOR
Emanuele Munarini, Mar 31 2003
STATUS
approved