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A264151
Row sums of A179455.
2
1, 1, 3, 12, 63, 398, 2911, 24177, 224824, 2313892, 26107679, 320412404, 4249353369, 60561549764, 923107802463, 14985538729504, 258138422935578, 4702896016961154, 90350619640638353, 1825564783445799571, 38700814850328413380, 858915876402686598209, 19916917035087719607321
OFFSET
0,3
LINKS
Swapnil Garg, Alan Peng, Classical and consecutive pattern avoidance in rooted forests, arXiv:2005.08889 [math.CO], May 2020.
Peter Luschny, Permutation Trees
FORMULA
a(n) = Sum_{k=0..n} (n-k+1)*A179454(n,k), where A179454(n,k) is read as a (0,0)-based table with an additional column (1,0,0,0,...) at the left hand side.
EXAMPLE
a(4) = 5*0 + 4*1 + 3*14 + 2*8 + 1*1 = 63.
PROG
(Sage) # uses[bell_transform from A264428]
def A264151_list(len):
b = [1]+[0]*(len-1); L = [b]
for k in range(len):
b = [sum((bell_transform(n, b))) for n in range(len)]
L.append(b)
return [sum(L[k][n] for k in (0..n)) for n in range(len)]
print(A264151_list(10))
CROSSREFS
KEYWORD
nonn
AUTHOR
Peter Luschny, Dec 06 2015
STATUS
approved