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A258473 Number of partitions of n into two sorts of parts having exactly 3 parts of the second sort.

%I A258473 #7 Dec 11 2020 06:14:18
%S A258473 1,5,16,41,91,186,351,635,1090,1824,2939,4652,7162,10875,16159,23758,
%T A258473 34321,49145,69389,97213,134608,185172,252182,341443,458413,612186,
%U A258473 811567,1070826,1403784,1832370,2378320,3074642,3954869,5068684,6466697,8222640,10412903
%N A258473 Number of partitions of n into two sorts of parts having exactly 3 parts of the second sort.
%H A258473 Alois P. Heinz, <a href="/A258473/b258473.txt">Table of n, a(n) for n = 3..1000</a>
%p A258473 b:= proc(n, i) option remember; series(`if`(n=0, 1,
%p A258473       `if`(i<1, 0, add(b(n-i*j, i-1)*add(x^t*
%p A258473        binomial(j, t), t=0..min(3, j)), j=0..n/i))), x, 4)
%p A258473     end:
%p A258473 a:= n-> coeff(b(n$2), x, 3):
%p A258473 seq(a(n), n=3..40);
%t A258473 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[3, j]}], {j, 0, n/i}]]], {x, 0, 4}];
%t A258473 a[n_] := Coefficient[b[n, n], x, 3];
%t A258473 a /@ Range[3, 40] (* _Jean-François Alcover_, Dec 11 2020, after _Alois P. Heinz_ *)
%Y A258473 Column k=3 of A256193.
%K A258473 nonn
%O A258473 3,2
%A A258473 _Alois P. Heinz_, May 31 2015