A264151 Row sums of A179455.

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

Vaclav Kotesovec, Table of n, a(n) for n = 0..447

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

Cf. A179454, A179455, A264428.

Sequence in context: A020123 A307708 A308206 * A186186 A355164 A373770

Adjacent sequences: A264148 A264149 A264150 * A264152 A264153 A264154

Keyword

nonn

Author

Peter Luschny, Dec 06 2015

Status

approved