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

Author

Peter Luschny, Dec 06 2015

Keywords

• nonn

Examples

			a(4) = 5*0 + 4*1 + 3*14 + 2*8 + 1*1 = 63.
		

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

Crossrefs

Cf. A179454, A179455, A264428.

Programs

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))

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.