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A258475 Number of partitions of n into two sorts of parts having exactly 5 parts of the second sort.

%I A258475 #7 Dec 11 2020 05:59:27
%S A258475 1,7,29,92,247,590,1291,2642,5114,9475,16882,29159,48914,80160,128405,
%T A258475 201958,311878,474540,711222,1052949,1539214,2226774,3186866,4520230,
%U A258475 6351925,8856519,12248350,16822982,22940863,31092121,41871405,56078299,74676693,98949447
%N A258475 Number of partitions of n into two sorts of parts having exactly 5 parts of the second sort.
%H A258475 Alois P. Heinz, <a href="/A258475/b258475.txt">Table of n, a(n) for n = 5..1000</a>
%p A258475 b:= proc(n, i) option remember; series(`if`(n=0, 1,
%p A258475       `if`(i<1, 0, add(b(n-i*j, i-1)*add(x^t*
%p A258475        binomial(j, t), t=0..min(5, j)), j=0..n/i))), x, 6)
%p A258475     end:
%p A258475 a:= n-> coeff(b(n$2), x, 5):
%p A258475 seq(a(n), n=5..40);
%t A258475 b[n_, i_] := b[n, i] = Series[If[n==0, 1, If[i<1, 0, Sum[b[n-i*j, i-1]*Sum[ x^t*Binomial[j, t], {t, 0, Min[5, j]}], {j, 0, n/i}]]], {x, 0, 6}];
%t A258475 a[n_] := Coefficient[b[n, n], x, 5];
%t A258475 a /@ Range[5, 40] (* _Jean-François Alcover_, Dec 11 2020, after _Alois P. Heinz_ *)
%Y A258475 Column k=5 of A256193.
%K A258475 nonn
%O A258475 5,2
%A A258475 _Alois P. Heinz_, May 31 2015