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A170911 Write exp(-x) = Product_{n>=1} (1 + g_n x^n); a(n) = denominator(g_n). 5

%I

%S 1,2,3,8,5,72,7,128,81,800,11,13824,13,6272,30375,32768,17,419904,19,

%T 20480000,750141,247808,23,1528823808,15625,1384448,1594323,

%U 5035261952,29,30233088000000,31,2147483648,235782657,37879808,1313046875,240734712102912,37,189267968

%N Write exp(-x) = Product_{n>=1} (1 + g_n x^n); a(n) = denominator(g_n).

%H H. Gingold, H. W. Gould, and Michael E. Mays, <a href="https://www.researchgate.net/publication/268023169_Power_product_expansions">Power Product Expansions</a>, Utilitas Mathematica 34 (1988), 143-161.

%e -1, 1/2, 1/3, 3/8, 1/5, 13/72, 1/7, 27/128, 8/81, 91/800, 1/11, ...

%p L:=100; t1:=exp(-x); t0:=series(t1,x,L): g:=[]; M:=40; t2:=t0:

%p for n from 1 to M do t3:=coeff(t2,x,n); t2:=series(t2/(1+t3*x^n),x,L); g:=[op(g),t3]; od: g;

%Y Cf. A170910 (numerators).

%K nonn,frac

%O 1,2

%A _N. J. A. Sloane_, Jan 30 2010

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Last modified October 27 15:27 EDT 2021. Contains 348287 sequences. (Running on oeis4.)