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%I #10 Jun 07 2019 12:58:02
%S 1,2,10,68,574,5732,65724,847800,12120966,189890588,3230531356,
%T 59246895512,1164225730540,24387062160008,542155626123544,
%U 12743158072837680,315624979700257350,8213507146488950700
%N A sum of Lah numbers and binomial coefficients.
%F Formula: a(n) = Sum[ Lah[ n, k ] binomial[ 2 k, k ], { k, 0, n } ] where Lah[n, k] = binomial[ n - 1, k - 1 ] n! / k! are the Lah numbers. Recurrence: ( n + 3 ) a(n+3) - ( 3 n^2 + 17 n + 24 ) a(n+2) + 3 ( n + 3 )( n + 2 )( n + 1 ) a(n+1) - ( n + 2 )( n + 1 )^2 n a(n) = 0
%F E.g.f.: BesselI(0, 2*x/(1-x))*exp(2*x/(1-x)). - _Vladeta Jovovic_, Sep 13 2003
%F a(n) ~ exp(4*sqrt(n) - n - 2) * n^(n - 1/2) / sqrt(2*Pi). - _Vaclav Kotesovec_, Jun 07 2019
%t RecurrenceTable[{-(-3 + n) (-2 + n)^2 (-1 + n) a[-3 + n] + 3 (-2 + n) (-1 + n) n a[-2 + n] - n (-1 + 3 n) a[-1 + n] + n a[n] == 0, a[0] == 1, a[1] == 2, a[2] == 10}, a, {n, 0, 20}] (* _Vaclav Kotesovec_, Jun 07 2019 *)
%K easy,nonn
%O 0,2
%A _Emanuele Munarini_, May 07 2003
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