A381752 - OEIS

%I #9 Mar 06 2025 08:27:54

%S 1,9,525,44067,4338765,467396050,53346810991,6339179481480,

%T 775994115988525,97182642466115275,12392633418043399130,

%U 1603634650155295053250,210047857493659698690575,27795006677556725604853840,3710220786174094422360657000,498998879378383167317202612400

%N Expansion of exp( Sum_{k>=1} binomial(10*k-1,2*k-1) * x^k/k ).

%F a(0) = 1; a(n) = (1/n) * Sum_{k=1..n} binomial(10*k-1,2*k-1) * a(n-k).

%o (PARI) my(N=20, x='x+O('x^N)); Vec(exp(sum(k=1, N, binomial(10*k-1, 2*k-1)*x^k/k)))

%Y Cf. A006013, A079489, A182960, A381751, A381753, A381757, A381758.

%Y Cf. A381746.

%K nonn,easy

%O 0,2

%A _Seiichi Manyama_, Mar 06 2025