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A206848 G.f.: exp( Sum_{n>=1} x^n/n * Sum_{k=0..n} binomial(n^2, k^2) ). 6

%I #14 Jan 19 2019 07:03:18

%S 1,2,5,53,3422,826606,1335470713,9548109569885,190076214495558260,

%T 18558289189760778318731,10286810587274357297985552184,

%U 16301371794177939084545371104827679,91249944361047494534207504939405352235731,3283593155431496336538359592977826684908598341441

%N G.f.: exp( Sum_{n>=1} x^n/n * Sum_{k=0..n} binomial(n^2, k^2) ).

%C Logarithmic derivative yields A206849.

%C Equals row sums of triangle A228902.

%H Seiichi Manyama, <a href="/A206848/b206848.txt">Table of n, a(n) for n = 0..57</a>

%e G.f.: A(x) = 1 + 2*x + 5*x^2 + 53*x^3 + 3422*x^4 + 826606*x^5 + 1335470713*x^6 +...

%e where the logarithm of the g.f. yields the l.g.f. of A206849:

%e log(A(x)) = 2*x + 6*x^2/2 + 137*x^3/3 + 13278*x^4/4 + 4098627*x^5/5 +...

%o (PARI) {a(n)=polcoeff(exp(sum(m=1, n, sum(k=0, m, binomial(m^2,k^2))*x^m/m)+x*O(x^n)), n)}

%o for(n=0, 25, print1(a(n), ", "))

%Y Cf. A206849 (log), A206846, A206850, A228902.

%Y Cf. variants: A167006, A228809.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Feb 15 2012

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