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A118789
Row sums of triangle A118788.
2
1, 2, 9, 71, 800, 11659, 208173, 4398148, 107293711, 2967800711, 91777098006, 3137581240925, 117499040544197, 4783424590188490, 210333509575901445, 9934472399437068811, 501615620424564184408, 26963169913347131361647
OFFSET
0,2
COMMENTS
A032188 equals the main diagonal of triangle A118788; A032188(n) = number of labeled series-reduced mobiles (circular rooted trees) with n leaves.
FORMULA
E.g.f.: A(x) = exp( Sum_{n>=1} A032188(n)*x^n/n! ). As row sums of A118788, a(n) = Sum_{k=0..n} n!/(n-k)!*[x^k]{ x/(2*x + log(1-x)) }^(n+1).
EXAMPLE
E.g.f.: A(x) = 1 + 1*x + 2*x^2/2! + 9*x^3/3! + 71*x^4/4! + ... =
exp(x + x^2/2! + 5*x^3/3! + 41*x^4/4! +... + A032188(n)*x^n/n! +...).
PROG
(PARI)
{a(n)=local(x=X+X^2*O(X^n)); sum(k=0, n, n!/(n-k)!*polcoeff((x/(2*x+log(1-x)))^(n+1), k, X))}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Apr 29 2006
STATUS
approved