A327552 - OEIS

%I #15 Dec 17 2020 11:56:16

%S 0,1,2,7,11,29,63,125,225,489,930,1704,3260,5859,10868,20026,35062,

%T 61660,111789,191119,337432,585847,1003876,1705380,2921394,4930357,

%U 8311554,14013583,23435178,38849655,64847870,106784912,175699558,289676875,472418418,772944773

%N Number of partitions in all twice partitions of n where the first partition is strict.

%H Alois P. Heinz, <a href="/A327552/b327552.txt">Table of n, a(n) for n = 0..3200</a>

%e a(3) = 7 = 1+1+1+2+2 counting the partitions in 3, 21, 111, 2|1, 11|1.

%p b:= proc(n, i) option remember; `if`(i*(i+1)/2<n, 0,

%p       `if`(n=0, [1, 0], b(n, i-1)+(p->p+[0, p[1]])(

%p       combinat[numbpart](i)*b(n-i, min(n-i, i-1)))))

%p     end:

%p a:= n-> b(n$2)[2]:

%p seq(a(n), n=0..36);

%t b[n_, i_] := b[n, i] = If[i(i+1)/2<n, {0, 0}, If[n==0, {1, 0}, b[n, i-1] + Function[p, p + {0, p[[1]]}][PartitionsP[i] b[n-i, Min[n-i, i-1]]]]];

%t a[n_] := b[n, n][[2]];

%t a /@ Range[0, 36] (* _Jean-François Alcover_, Dec 17 2020, after _Alois P. Heinz_ *)

%Y Cf. A000009, A000041, A271619, A327607.

%K nonn

%O 0,3

%A _Alois P. Heinz_, Sep 16 2019