|
|
A075923
|
|
Fourth column of triangle A075502.
|
|
2
|
|
|
1, 70, 3185, 120050, 4084101, 130590390, 4012419145, 120031392250, 3525181576301, 102196720335710, 2935410756419505, 83751552660170850, 2377917929557166101, 67273652916778177030, 1898215473677945050265
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
The e.g.f. given below is Sum_{m=0..3} A075513(4,m)*exp(7*(m+1)*x)/3!.
|
|
LINKS
|
|
|
FORMULA
|
a(n) = A075502(n+4, 4) = (7^n)*S2(n+4, 4) with S2(n, m) := A008277(n, m) (Stirling2).
a(n) = (-7^n + 24*14^n - 81*21^n + 64*28^n)/3!.
G.f.: 1/Product_{k=1..4} (1 - 7*k*x).
E.g.f.: (d^4/dx^4)(((exp(7*x)-1)/7)^4)/4! = (-exp(7*x) + 24*exp(14*x) - 81*exp(21*x) + 64*exp(28*x))/3!.
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|