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#16 by Vaclav Kotesovec at Sat Dec 05 05:51:45 EST 2020
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#15 by Vaclav Kotesovec at Sat Dec 05 05:51:21 EST 2020
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a(n) ~ c * 4^n, where c = Product_{k>=1} 1/(1-1/4^k) = A065446 * A132020 = 1.4523536424495970158347... . - Vaclav Kotesovec, Mar 19 2015
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proposed
editing
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#14 by Jean-François Alcover at Sat Dec 05 04:15:11 EST 2020
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#13 by Jean-François Alcover at Sat Dec 05 04:14:58 EST 2020
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b[n_, i_] := b[n, i] = If[n==0, 1, If[i<1, 0, b[n, i-1]+If[i>n, 0, 4 b[n-i, i]]]];
a[n_] := b[n, n];
a /@ Range[0, 25] (* Jean-François Alcover, Dec 05 2020, after Alois P. Heinz *)
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approved
editing
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#12 by Susanna Cuyler at Thu Apr 12 22:23:16 EDT 2018
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#11 by Ilya Gutkovskiy at Thu Apr 12 16:12:27 EDT 2018
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#10 by Ilya Gutkovskiy at Thu Apr 12 13:58:59 EDT 2018
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G.f.: Sum_{i>=0} 4^i*x^i/Product_{j=1..i} (1 - x^j). - Ilya Gutkovskiy, Apr 12 2018
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approved
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#9 by Bruno Berselli at Sat Nov 21 00:45:23 EST 2015
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#8 by Vladimir Reshetnikov at Fri Nov 20 20:48:02 EST 2015
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#7 by Vladimir Reshetnikov at Fri Nov 20 20:48:00 EST 2015
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| MATHEMATICA
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(O[x]^20 - 3/QPochhammer[4, x])[[3]] (* Vladimir Reshetnikov, Nov 20 2015 *)
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approved
editing
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