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 A125813 q-Bell numbers for q=3; eigensequence of A022167, which is the triangle of Gaussian binomial coefficients [n,k] for q=3. 6
 1, 1, 2, 7, 47, 628, 17327, 1022983, 132615812, 38522717107, 25526768401271, 39190247441314450, 141213238745969102393, 1207367655155905204747681, 24733467452839301566047854678, 1224709126636123500201799360630423 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS FORMULA a(n) = Sum_{k=0..n-1} A022167(n-1,k) * a(k) for n>0, with a(0)=1. EXAMPLE The recurrence: a(n) = Sum_{k=0..n-1} A022167(n-1,k) * a(k) is illustrated by: a(2) = 1*(1) + 4*(1) + 1*(2) = 7; a(3) = 1*(1) + 13*(1) + 13*(2) + 1*(7) = 47; a(4) = 1*(1) + 40*(1) + 130*(2) + 40*(7) + 1*(47) = 628. Triangle A022167 begins: 1; 1, 1; 1, 4, 1; 1, 13, 13, 1; 1, 40, 130, 40, 1; 1, 121, 1210, 1210, 121, 1; 1, 364, 11011, 33880, 11011, 364, 1; ... PROG (PARI) /* q-Binomial coefficients: */ C_q(n, k)=if(n

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Last modified January 20 10:18 EST 2022. Contains 350471 sequences. (Running on oeis4.)