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%I #11 Jan 22 2024 22:27:19
%S 1,1,2,10,64,704,8704,160768,3146240,85459456,2379068416,87838524416,
%T 3254378586112,155039348776960,7304909102465024,432732882146443264,
%U 25086801102965899264,1797560686374797508608,125049014505246260592640
%N a(0)=1; a(1)=1; for a>1, a(n)=a(n-1)+((n-1)^3)*a(n-2).
%C For n>0, a(n+1)=A166469(A167448(n)).
%H Harvey P. Dale, <a href="/A167449/b167449.txt">Table of n, a(n) for n = 0..321</a>
%F a(n) ~ (c1 + c2*(-1)^n) * n^(3*n/2) / exp(3*n/2), where c1 = 11.229547293548917938785936532203403620187829245793... and c2 = -0.20385401969014506196353281640163785658756407221649... - _Vaclav Kotesovec_, Aug 10 2021
%t RecurrenceTable[{a[n] == a[n-1] + (n-1)^3*a[n-2], a[0] == 1, a[1] == 1}, a, {n, 0, 20}] (* _Vaclav Kotesovec_, Aug 08 2021 *)
%t nxt[{n_,a_,b_}]:={n+1,b,b+n^3 a}; NestList[nxt,{1,1,1},20][[;;,2]] (* _Harvey P. Dale_, Jan 22 2024 *)
%Y Other sequences for which a(n)=a(n-1)+((n-1)^k)*a(n-2) are (k=0) A000045, (k=1) A000085, (k=2) A000142.
%K nonn
%O 0,3
%A _Matthew Vandermast_, Nov 09 2009
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