%I #11 Nov 22 2022 13:50:35
%S 0,1,2,4,10,31,110,421,1686,6961,29392,126292,550360,2426503,10803802,
%T 48507844,219377950,998436793,4569488372,21016589074,97090411020,
%U 450314942683,2096122733212,9788916220519,45850711498860,215348942668681,1013979873542690,4785437476592806
%N Binomial transform of A000957.
%H Harvey P. Dale, <a href="/A138415/b138415.txt">Table of n, a(n) for n = 0..1000</a>
%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%F From _Vaclav Kotesovec_, Oct 30 2017: (Start)
%F Recurrence: 2*n*a(n) = 3*(5*n - 6)*a(n-1) - (29*n - 57)*a(n-2) + 3*(7*n - 18)*a(n-3) - 5*(n-3)*a(n-4).
%F a(n) ~ 5^(n + 3/2) / (72 * sqrt(Pi) * n^(3/2)). (End)
%t Table[Sum[Binomial[n, k]*(2^k * (2*k-1)!! * Hypergeometric2F1Regularized[2, 2*k+1, k+2, -1] - 3*(-1)^k/2^(k+1)), {k, 1, n}], {n, 0, 30}] (* _Vaclav Kotesovec_, Oct 30 2017 *)
%t RecurrenceTable[{a[0]==0,a[1]==1,a[2]==2,a[3]==4,a[n]==(3(5n-6)a[n-1]-(29n-57) a[n-2]+3(7n-18)a[n-3]-5(n-3)a[n-4])/(2n)},a,{n,30}] (* _Harvey P. Dale_, Nov 22 2022 *)
%Y Cf. A000957, A138461.
%K nonn
%O 0,3
%A _N. J. A. Sloane_, May 08 2008