|
|
A075506
|
|
Shifts one place left under 7th-order binomial transform.
|
|
7
|
|
|
1, 1, 8, 71, 729, 8842, 125399, 2026249, 36458010, 719866701, 15453821461, 358100141148, 8899677678109, 235877034446341, 6634976621814472, 197269776623577659, 6177654735731310917, 203136983117907790890, 6994626418539177737803, 251584328242318030774781
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
COMMENTS
|
Previous name was: Row sums of triangle A075502 (for n>=1).
|
|
LINKS
|
|
|
FORMULA
|
a(n) = sum((7^(n-m))*S2(n,m), m=0..n), with S2(n,m) = A008277(n,m) (Stirling2).
E.g.f.: exp((exp(7*x)-1)/7).
O.g.f.: Sum_{k>=0} x^k/Product_{j=1..k} (1 - 7*j*x). - Ilya Gutkovskiy, Mar 20 2018
a(n) ~ 7^n * n^n * exp(n/LambertW(7*n) - 1/7 - n) / (sqrt(1 + LambertW(7*n)) * LambertW(7*n)^n). - Vaclav Kotesovec, Jul 15 2021
|
|
MAPLE
|
[seq(factorial(k)*coeftayl(exp((exp(7*x)-1)/7), x = 0, k), k=0..20)]; # Muniru A Asiru, Mar 20 2018
|
|
MATHEMATICA
|
Table[7^n BellB[n, 1/7], {n, 0, 20}]
|
|
PROG
|
(GAP) List([0..20], n->Sum([0..n], m->7^(n-m)*Stirling2(n, m))); # Muniru A Asiru, Mar 20 2018
|
|
CROSSREFS
|
Shifts one place left under k-th order binomial transform, k=1..10: A000110, A004211, A004212, A004213, A005011, A005012, A075506, A075507, A075508, A075509.
|
|
KEYWORD
|
nonn,easy,eigen
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|