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Number of partitions of n into an odd number of parts, the least being 5; also, a(n+5) = number of partitions of n into an even number of parts, each >=5.
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%I #20 May 15 2023 11:13:24

%S 0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,1,2,2,3,3,4,4,5,5,7,7,9,10,13,14,18,20,

%T 25,28,35,39,48,54,65,74,89,100,119,135,160,181,213,241,282,320,372,

%U 422,490,554,641,726,836,946,1087,1229,1408,1591,1817,2052,2341,2639,3002,3384

%N Number of partitions of n into an odd number of parts, the least being 5; also, a(n+5) = number of partitions of n into an even number of parts, each >=5.

%F a(n) = A026798(n) - A027197(n). - _Jean-François Alcover_, Feb 06 2020

%F G.f.: x^5 * Sum_{k>=0} x^(10*k)/Product_{j=1..2*k} (1-x^j). - _Seiichi Manyama_, May 15 2023

%t b[n_, i_, t_] := b[n, i, t] = If[n == 0, t, If[i > n, 0, b[n, i + 1, t] + b[n - i, i, 1 - t]]];

%t a027197[n_] := If[n < 5, 0, b[n - 5, 5, 0]];

%t a026798[n_] := SeriesCoefficient[x^5/QPochhammer[x^5, x], {x, 0, n}];

%t a[n_] := a026798[n] - a027197[n];

%t a /@ Range[55] (* _Jean-François Alcover_, Feb 06 2020, after _Alois P. Heinz_ in A027197 *)

%Y Cf. A026798, A027197.

%K nonn

%O 1,17

%A _Clark Kimberling_

%E More terms from _Seiichi Manyama_, May 15 2023