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URL: https://oeis.org/A196834

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A196834
Row sums of Sheffer triangle A193685 (5-restricted Stirling2 numbers).
7
1, 6, 37, 235, 1540, 10427, 73013, 529032, 3967195, 30785747, 247126450, 2050937445, 17585497797, 155666739742, 1421428484337, 13377704321695, 129659127547372, 1293095848212799, 13259069937250169, 139671750579429512, 1510382932875294447, 16754464511605466311
OFFSET
0,2
LINKS
FORMULA
a(n) = Sum_{m=0..n} A193685(n,m).
E.g.f.: exp(exp(x)+5*x-1).
a(n) ~ exp(n/LambertW(n) - n - 1) * n^(n + 5) / LambertW(n)^(n + 11/2). - Vaclav Kotesovec, Jun 10 2020
a(0) = 1; a(n) = 5 * a(n-1) + Sum_{k=0..n-1} binomial(n-1,k) * a(k). - Ilya Gutkovskiy, Jul 03 2020
EXAMPLE
a(2) = 25 + 11 + 1 = 37.
MAPLE
b:= proc(n, m) option remember;
`if`(n=0, 1, m*b(n-1, m)+b(n-1, m+1))
end:
a:= n-> b(n, 5):
seq(a(n), n=0..23); # Alois P. Heinz, Aug 22 2021
MATHEMATICA
nmax = 20; CoefficientList[Series[E^(E^x + 5*x - 1), {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Jun 10 2020 *)
CROSSREFS
Cf. A000110, A005493, A005494, A045379, A196835 (alternating row sums).
Sequence in context: A081188 A218186 A154623 * A005389 A080954 A271905
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Oct 07 2011
STATUS
approved