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A049377 Row sums of triangle A049352. 6
1, 1, 5, 33, 273, 2721, 31701, 421905, 6302913, 104270913, 1889862021, 37204038081, 789866524305, 17977594555233, 436435929785493, 11251798888929201, 306889765901872641, 8825681949708120705, 266828094135981378693, 8458295877281844310113 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
W. Lang, On generalizations of Stirling number triangles, J. Integer Seqs., Vol. 3 (2000), #00.2.4.
FORMULA
E.g.f. exp(p(x)) with p(x) := x*(3-3*x+x^2)/(3*(1-x)^3) (E.g.f. first column of A049352).
a(n) ~ n^(n-1/8)/2 * exp(-1/4 + 5*n^(1/4)/24 + sqrt(n)/2 + 4*n^(3/4)/3 - n). - Vaclav Kotesovec, Oct 23 2017
E.g.f.: Sum_{n>=0} ( Integral 1/(1-x)^4 dx )^n / n!, where the constant of integration is taken to be zero. - Paul D. Hanna, Apr 27 2019
MAPLE
a:= proc(n) option remember; `if`(n=0, 1, add(
binomial(n-1, j-1)*(j+2)!/6*a(n-j), j=1..n))
end:
seq(a(n), n=0..25); # Alois P. Heinz, Aug 01 2017
MATHEMATICA
a[0] = 1; a[n_] := a[n] = Sum[Binomial[n-1, j-1]*(j+2)!/6*a[n-j], {j, 1, n}];
Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Jun 04 2018, after Alois P. Heinz *)
CROSSREFS
Cf. A049352.
Sequence in context: A269820 A302075 A215671 * A325153 A129890 A316158
KEYWORD
nonn
AUTHOR
EXTENSIONS
a(0)=1 prepended by Alois P. Heinz, Aug 01 2017
STATUS
approved

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Last modified April 25 11:24 EDT 2024. Contains 371967 sequences. (Running on oeis4.)