A033842 -id:A033842 - cp's OEIS frontend

A049351 Row sums of triangle A049327.

1, 16, 151, 1051, 7072, 52189, 387961, 2803408, 20262175, 147578083, 1074220864, 7803627829, 56703899473, 412249980976, 2996844053479, 21782472167851, 158330928308704, 1150906042354381, 8365826645067625, 60809849516721040

Offset: 1

Wolfdieter Lang

p(5,x) is row polynomial corresponding to triangle row A033842(5,m).

W. Lang, On generalizations of Stirling number triangles, J. Integer Seqs., Vol. 3 (2000), #00.2.4.

Cf. A033842, A049327.

G.f. x*p(5, x)/(1-x*p(5, x)) with x*p(5, x)= x*(1+15*x+120*x^2+540*x^3+1296*x^4+1296*x^5 ) G.f. for first column of A049327.

A173249 Partial sums of A000272.

Original entry on oeis.org

1, 2, 3, 6, 22, 147, 1443, 18250, 280394, 5063363, 105063363, 2463011054, 64380375278, 1856540769315, 58550453144611, 2004745521503986, 74062339559431922, 2936485391069247715, 124376016487663499491

Offset: 0

Jonathan Vos Post, Feb 13 2010

Partial sums of number of trees on n labeled nodes. The subsequence of primes in this sequence begin: 2, 58550453144611, no more through a(30).

			a(19) = 1 + 1 + 1 + 3 + 16 + 125 + 1296 + 16807 + 262144 + 4782969 + 100000000 + 2357947691 + 61917364224 + 1792160394037 + 56693912375296 + 1946195068359375 + 72057594037927936 + 2862423051509815793 + 121439531096594251776 + 5480386857784802185939.

Cf. A000055, A000169, A000312, A007778, A007830, A008785-A008791, A033842, A000272, A036361, A036362, A036506, A000055, A054581, A097170

a(n) = SUM[i=0..n] A000272(i) = SUM[i=0..n] i^(i-2).

cp's OEIS Frontend

A049351 Row sums of triangle A049327.

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