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G.f.: exp( Sum_{n>=1} x^n/n * Sum_{k=0..n} binomial(n*k, k^2) ).
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%I #14 Jan 19 2019 07:03:51

%S 1,2,4,12,94,2195,158904,31681195,13904396167,15305894726347,

%T 44888344014554903,288228807835914177564,4270880356112396772814732,

%U 169380654509201278629725097906,15394658527137259981745081997280638,3042352591056504014301304188228238554499

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

%C Logarithmic derivative equals A228808.

%C Equals row sums of triangle A228904.

%H Seiichi Manyama, <a href="/A228809/b228809.txt">Table of n, a(n) for n = 0..73</a>

%e G.f.: A(x) = 1 + 2*x + 4*x^2 + 12*x^3 + 94*x^4 + 2195*x^5 +...

%e where

%e log(A(x)) = 2*x + 4*x^2/2 + 20*x^3/3 + 296*x^4/4 + 10067*x^5/5 + 927100*x^6/6 +...+ A228808(n)*x^n/n +...

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

%o for(n=0, 20, print1(a(n), ", "))

%Y Cf. A228808, A207135, A228904.

%Y Cf. variants: A167006, A206848.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Sep 04 2013