|
Search: id:A081143
|
|
|
| A081143 |
|
5-th binomial transform of (0,0,0,1,0,0,0,0,......). |
|
+0
3
|
|
| 0, 0, 0, 1, 20, 250, 2500, 21875, 175000, 1312500, 9375000, 64453125, 429687500, 2792968750, 17773437500, 111083984375, 683593750000, 4150390625000, 24902343750000, 147857666015625, 869750976562500, 5073547363281250
(list; graph; listen)
|
|
|
OFFSET
|
0,5
|
|
|
COMMENT
|
Starting at 1, four-fold convolution of A000351 (powers of 5).
With a different offset, number of n-permutations (n=4)of 6 objects u, v, w, z, x, y with repetition allowed, containing exactly three u's. Example: a(4)=20 because we have uuuv, uuvu, uvuu, vuuu, uuuw, uuwu, uwuu, wuuu, uuuz, uuzu, uzuu, zuuu, uuux, uuxu, uxuu, xuuu, uuuy, uuyu, uyuu and yuuu - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 03 2008
|
|
FORMULA
|
a(n)=20a(n-1)-150a(n-2)+500a(n-3)-625a(n-4), a(0)=a(1)=a(2)=0, a(3)=1. a(n)=5^(n-3)C(n, 3). G.f. x^3/(1-5x)^4.
|
|
MAPLE
|
seq(binomial(n+3, 3)*5^n, n=-3..18); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 03 2008
|
|
CROSSREFS
|
Cf. A038846, A036216, A001789, A081144, A081135.
Adjacent sequences: A081140 A081141 A081142 this_sequence A081144 A081145 A081146
Sequence in context: A125432 A055757 A022744 this_sequence A075469 A028032 A025986
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
Paul Barry (pbarry(AT)wit.ie), Mar 08 2003
|
|
|
Search completed in 0.002 seconds
|
