This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A381744 #19 Mar 06 2025 08:15:55
%S A381744 1,10,215,5942,186111,6283192,222992692,8201608382,309834609743,
%T A381744 11950890428170,468707758663887,18634632264615272,749325132218313540,
%U A381744 30422303269317412048,1245346665979469486376,51343805279989437688334,2130090659402456357279919,88858984785475871013971710
%N A381744 Expansion of exp( Sum_{k>=1} binomial(6*k-1,2*k) * x^k/k ).
%H A381744 Seiichi Manyama, <a href="/A381744/b381744.txt">Table of n, a(n) for n = 0..605</a>
%F A381744 G.f. A(x) satisfies A(x^2) = B(x) * B(-x), where B(x) is the g.f. of A006013.
%F A381744 a(n) = Sum_{k=0..2*n} (-1)^k * A006013(k) * A006013(2*n-k).
%F A381744 a(0) = 1; a(n) = (1/n) * Sum_{k=1..n} binomial(6*k-1,2*k) * a(n-k).
%F A381744 G.f.: B(x)^2, where B(x) is the g.f. of A182960.
%o A381744 (PARI) my(N=20, x='x+O('x^N)); Vec(exp(sum(k=1, N, binomial(6*k-1, 2*k)*x^k/k)))
%Y A381744 Cf. A079489, A381745, A381746.
%Y A381744 Cf. A006013, A182960.
%K A381744 nonn,easy
%O A381744 0,2
%A A381744 _Seiichi Manyama_, Mar 05 2025