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A206155
G.f.: exp( Sum_{n>=1} A206156(n)*x^n/n ), where A206156(n) = Sum_{k=0..n} binomial(n,k)^(2*k).
3
1, 2, 5, 38, 1425, 283002, 448468978, 2707673843860, 67018498701021670, 14506787732148113566364, 13603174532364904984495776225, 43960529641219941452921634596223366, 1207327102995668834632770987833295579308107, 188859837731175560954429490131760211759694331013582
OFFSET
0,2
COMMENTS
Logarithmic derivative yields A206156.
EXAMPLE
G.f.: A(x) = 1 + 2*x + 5*x^2 + 38*x^3 + 1425*x^4 + 283002*x^5 +...
where the logarithm of the g.f. begins:
log(A(x)) = 2*x + 6*x^2/2 + 92*x^3/3 + 5410*x^4/4 + 1400652*x^5/5 + 2687407464*x^6/6 +...+ A206156(n)*x^n/n +...
PROG
(PARI) {a(n)=polcoeff(exp(sum(m=1, n+1, x^m/m*sum(k=0, m, binomial(m, k)^(2*k-0))+x*O(x^n))), n)}
for(n=0, 16, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Feb 04 2012
STATUS
approved