|
|
A096341
|
|
E.g.f.: exp(x)/(1-x)^7.
|
|
8
|
|
|
1, 8, 71, 694, 7421, 86276, 1084483, 14665106, 212385209, 3280842496, 53862855551, 936722974958, 17205245113141, 332864226563324, 6766480571358971, 144202473398010826, 3215159679583864433
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
Sum_{k=0..n} A094816(n,k)*x^k give A000522(n), A001339(n), A082030(n), A095000(n), A095177(n), A096307(n) for x = 1, 2, 3, 4, 5, 6 respectively.
|
|
LINKS
|
|
|
FORMULA
|
a(n) = Sum_{k = 0..n} A094816(n, k)*7^k.
a(n) = Sum_{k = 0..n} binomial(n, k)*(k+6)!/6!.
a(n) = (n+7)*a(n-1) - (n-1)*a(n-2) with a(0) = 1 and a(1) = 8.
First-order recurrence: P(n-1)*a(n) = n*P(n)*a(n-1) + 1 with a(0) = 1, where P(n) = n^6 + 15*n^5 + 100*n^4 + 355*n^3 + 694*n^2 + 689*n + 265 = A094795(n).
(End)
|
|
MATHEMATICA
|
With[{nn = 250}, CoefficientList[Series[Exp[x]/(1 - x)^7, {x, 0, nn}], x] Range[0, nn]!] (* G. C. Greubel, May 27 2016 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|