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 A125812 q-Bell numbers for q=2; eigensequence of A022166, which is the triangle of Gaussian binomial coefficients [n,k] for q=2. 6
 1, 1, 2, 6, 28, 204, 2344, 43160, 1291952, 63647664, 5218320672, 719221578080, 168115994031040, 67159892835119296, 46166133463916209792, 54941957091151982047616, 113826217192695041078973184 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS FORMULA a(n) = Sum_{k=0..n-1} A022166(n-1,k) * a(k) for n>0, with a(0)=1. EXAMPLE The recurrence a(n) = Sum_{k=0..n-1} A022166(n-1,k) * a(k) is illustrated by: a(2) = 1*(1) + 3*(1) + 1*(2) = 6; a(3) = 1*(1) + 7*(1) + 7*(2) + 1*(6) = 28; a(4) = 1*(1) + 15*(1) + 35*(2) + 15*(6) + 1*(28) = 204. Triangle A022166 begins: 1; 1, 1; 1, 3, 1; 1, 7, 7, 1; 1, 15, 35, 15, 1; 1, 31, 155, 155, 31, 1; 1, 63, 651, 1395, 651, 63, 1; ... MATHEMATICA a[0] = 1; a[n_] := a[n] = Sum[QBinomial[n-1, k, 2] a[k], {k, 0, n-1}]; Table[a[n], {n, 0, 16}] (* Jean-François Alcover, Apr 09 2016 *) PROG (PARI) /* q-Binomial coefficients: */ {C_q(n, k)=if(n

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Last modified August 6 18:25 EDT 2020. Contains 336256 sequences. (Running on oeis4.)