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A306188 Number of n-times strict partitions of n.

%I A306188 #14 Dec 08 2020 08:04:31
%S A306188 1,1,1,4,11,41,154,904,4927,35398,234454,1965976,16589885,157974740,
%T A306188 1480736877,16406078770,177232251249,2151696598160,25726133391191,
%U A306188 346746928400037,4607758596471426,67562340652906942,969200312705046531,15386051753617360150
%N A306188 Number of n-times strict partitions of n.
%H A306188 Alois P. Heinz, <a href="/A306188/b306188.txt">Table of n, a(n) for n = 0..480</a>
%p A306188 b:= proc(n, i, k) option remember; `if`(i*(i+1)/2<n, 0, `if`(n=0 or
%p A306188       k=0, 1, b(n, i-1, k)+b(i$2, k-1)*b(n-i, min(n-i, i-1), k)))
%p A306188     end:
%p A306188 a:= n-> b(n$3):
%p A306188 seq(a(n), n=0..25);
%t A306188 b[n_, i_, k_] := b[n, i, k] = If[i(i+1)/2 < n, 0, If[n == 0 || k == 0, 1, b[n, i - 1, k] + b[i, i, k - 1] b[n - i, Min[n - i, i - 1], k]]];
%t A306188 a[n_] := b[n, n, n];
%t A306188 a /@ Range[0, 25] (* _Jean-François Alcover_, Dec 08 2020, after _Alois P. Heinz_ *)
%Y A306188 Cf. A000009, A261280, A306187.
%K A306188 nonn
%O A306188 0,4
%A A306188 _Alois P. Heinz_, Jan 27 2019