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A218120
G.f.: A(x) = exp( Sum_{n>=1} A069865(n)/2*x^n/n ) where A069865(n) = Sum_{k=0..n} C(n,k)^6.
3
1, 1, 17, 260, 7244, 214257, 7593707, 287419304, 11745920475, 503237634257, 22503750152879, 1039694201489294, 49401095274561608, 2402478324494963930, 119201977436336120482, 6017223412990713126034, 308361587173800754305214, 16013543997544827365960598
OFFSET
0,3
COMMENTS
Compare to a g.f. of Catalan numbers (A000108):
exp( Sum_{n>=1} A000984(n)/2*x^n/n ) where A000984(n) = Sum_{k=0..n} C(n,k)^2.
FORMULA
Self-convolution equals A218119.
EXAMPLE
G.f.: A(x) = 1 + x + 17*x^2 + 260*x^3 + 7244*x^4 + 214257*x^5 + 7593707*x^6 +...
log(A(x)) = x + 33*x^2/2 + 730*x^3/3 + 27425*x^4/4 + 1015626*x^5/5 + 43437282*x^6/6 + 1924149396*x^7/7 +...+ A069865(n)/2*x^n/n +...
PROG
(PARI) {a(n)=polcoeff(exp(sum(m=1, n, sum(k=0, m, binomial(m, k)^6)/2*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