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A218119
G.f.: A(x) = exp( Sum_{n>=1} A069865(n)*x^n/n ) where A069865(n) = Sum_{k=0..n} C(n,k)^6.
4
1, 2, 35, 554, 15297, 451842, 15929824, 601077640, 24488754772, 1046792248856, 46718718597567, 2155032002133834, 102259392504591235, 4967499746642163574, 246231868462969357492, 12419324761881256326288, 635990044563649443993091, 33006906229799699591298070
OFFSET
0,2
COMMENTS
Compare to a g.f. of Catalan numbers (A000108):
exp( Sum_{n>=1} A000984(n)*x^n/n ) where A000984(n) = Sum_{k=0..n} C(n,k)^2.
FORMULA
Equals row sums of triangle A218116.
Self-convolution of A218120.
EXAMPLE
G.f.: A(x) = 1 + 2*x + 35*x^2 + 554*x^3 + 15297*x^4 + 451842*x^5 + 15929824*x^6 +...
log(A(x)) = 2*x + 66*x^2/2 + 1460*x^3/3 + 54850*x^4/4 + 2031252*x^5/5 + 86874564*x^6/6 + 3848298792*x^7/7 +...+ A069865(n)*x^n/n +...
PROG
(PARI) {a(n)=polcoeff(exp(sum(m=1, n, sum(k=0, m, binomial(m, k)^6)*x^m/m)+x*O(x^n)), n)}
for(n=0, 25, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Oct 21 2012
STATUS
approved