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A258474 Number of partitions of n into two sorts of parts having exactly 4 parts of the second sort.

%I A258474 #7 Dec 11 2020 06:12:40
%S A258474 1,6,22,63,155,342,700,1343,2463,4323,7361,12139,19581,30819,47697,
%T A258474 72388,108390,159752,232833,334917,477270,672589,940222,1301954,
%U A258474 1790117,2441168,3308341,4451294,5955870,7918574,10475192,13779096,18042899,23506156,30496836
%N A258474 Number of partitions of n into two sorts of parts having exactly 4 parts of the second sort.
%H A258474 Alois P. Heinz, <a href="/A258474/b258474.txt">Table of n, a(n) for n = 4..1000</a>
%p A258474 b:= proc(n, i) option remember; series(`if`(n=0, 1,
%p A258474       `if`(i<1, 0, add(b(n-i*j, i-1)*add(x^t*
%p A258474        binomial(j, t), t=0..min(4, j)), j=0..n/i))), x, 5)
%p A258474     end:
%p A258474 a:= n-> coeff(b(n$2), x, 4):
%p A258474 seq(a(n), n=4..40);
%t A258474 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[4, j]}], {j, 0, n/i}]]], {x, 0, 5}];
%t A258474 a[n_] := Coefficient[b[n, n], x, 4];
%t A258474 a /@ Range[4, 40] (* _Jean-François Alcover_, Dec 11 2020, after _Alois P. Heinz_ *)
%Y A258474 Column k=4 of A256193.
%K A258474 nonn
%O A258474 4,2
%A A258474 _Alois P. Heinz_, May 31 2015