# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a327550 Showing 1-1 of 1 %I A327550 #23 Apr 24 2021 09:55:41 %S A327550 1,2,8,24,80,224,704,1920,5632,15360,43008,114688,315392,827392, %T A327550 2211840,5767168,15138816,38928384,100925440,256901120,657457152, %U A327550 1660944384,4202692608,10527703040,26424115200,65699577856,163477192704,403995361280,998043025408 %N A327550 Number of compositions of partitions of 2n with exactly n compositions. %H A327550 Alois P. Heinz, Table of n, a(n) for n = 0..3129 %F A327550 a(n) = A327549(2n,n). %F A327550 a(n) ~ 2^n * exp(Pi*sqrt(2*n/3)) / (4*sqrt(3)*n). - _Vaclav Kotesovec_, Sep 19 2019 %F A327550 a(n) = A000041(n) * A000079(n). - _Alois P. Heinz_, Oct 08 2020 %F A327550 G.f.: Product_{k>=1} 1 / (1 - 2^k*x^k). - _Ilya Gutkovskiy_, Apr 24 2021 %p A327550 b:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1 or %p A327550 k<1, 0, b(n, i-1, k)+ 2^(i-1)*b(n-i, min(n-i, i), k-1))) %p A327550 end: %p A327550 a:= n-> b(2*n$2, n)-`if`(n=0, 0, b(2*n$2, n-1)): %p A327550 seq(a(n), n=0..40); %t A327550 Table[2^n * PartitionsP[n], {n, 0, 30}] (* _Vaclav Kotesovec_, Oct 02 2020 *) %Y A327550 Cf. A000041, A000079, A327549. %K A327550 nonn %O A327550 0,2 %A A327550 _Alois P. Heinz_, Sep 16 2019 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE