|
Search: id:A134558
|
|
|
| A134558 |
|
Array, a(n,k) = Gamma[n+1,k]*e^k, where Gamma[n,k] is the upper incomplete gamma function and e is the exponential constant 2.71828..., read by anti-diagonals... |
|
+0
1
|
|
| 1, 1, 1, 2, 2, 1, 6, 5, 3, 1, 24, 16, 10, 4, 1, 120, 65, 38, 17, 5, 1, 720, 326, 168, 78, 26, 6, 1, 5040, 1957, 872, 393, 142, 37, 7, 1
(list; table; graph; listen)
|
|
|
OFFSET
|
0,4
|
|
|
FORMULA
|
a(n,k) = Gamma[n+1,k]*e^k = Sum[m!*C(n,m)*k^(n-m),{m,0,n}. a(n,k) = n*a(n-1,k) + k^n for n,k > 0. E.g.f (by columns) is e^(kx)/(1-x). a(n,k) = the binomial transform by columns of a(n,k-1). Conjecture: a(n,k) = the permanent of the n by n matrix with k+1 on the main diagonal and 1 elsewhere.
|
|
CROSSREFS
|
Cf. a(n, 0) = A000142(n); a(n, 1) = A000522(n); a(n, 2) = A010842(n); a(n, 3) = A053486(n); a(n, 4) = A053487(n); a(n, 5) = A080954(n); a(n, 6) = A108869(n); a(1, k) = A000027(k+1); a(2, k) = A002522(k+1); a(n, n) = A063170(n); a(n, n+1) = A001865(n+1); a(n, n+2) = a001863(n+2).
Sequence in context: A108074 A127743 A125278 this_sequence A137381 A109316 A094587
Adjacent sequences: A134555 A134556 A134557 this_sequence A134559 A134560 A134561
|
|
KEYWORD
|
nonn,tabl
|
|
AUTHOR
|
Ross La Haye (rlahaye(AT)new.rr.com), Jan 22 2008
|
|
|
Search completed in 0.002 seconds
|
