|
|
A303488
|
|
a(n) = n! * [x^n] 1/(1 - 5*x)^(n/5).
|
|
3
|
|
|
1, 1, 14, 312, 9576, 375000, 17873856, 1004306688, 65006637696, 4763494479744, 389812500000000, 35237024762075136, 3487065897634615296, 374960171943074285568, 43532820293400237735936, 5427359437500000000000000, 723181462895975365595529216, 102563963819340862347122245632
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
LINKS
|
|
|
FORMULA
|
a(n) = Product_{k=0..n-1} (5*k + n).
a(n) = 5^n*Gamma(6*n/5)/Gamma(n/5).
a(n) ~ 6^(6*n/5-1/2)*n^n/exp(n).
|
|
EXAMPLE
|
a(1) = 1;
a(2) = 2*7 = 14;
a(3) = 3*8*13 = 312;
a(4) = 4*9*14*19 = 9576;
a(5) = 5*10*15*20*25 = 375000, etc.
|
|
MATHEMATICA
|
Table[n! SeriesCoefficient[1/(1 - 5 x)^(n/5), {x, 0, n}], {n, 0, 17}]
Table[Product[5 k + n, {k, 0, n - 1}], {n, 0, 17}]
Table[5^n Pochhammer[n/5, n], {n, 0, 17}]
|
|
CROSSREFS
|
Cf. A008546, A008548, A034300, A034301, A034323, A034325, A047055, A047056, A051687, A051688, A051689, A051690, A051691, A052562, A113551, A303486, A303487.
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|