|
| |
|
|
A187004
|
|
Expansion of A(x) = (1 + 2*x^2 + 6*x^3 + 9*x^4 + 8*x^5 + 5*x^6) / (1 - x - 2*x^2 - 3*x^3 - 3*x^4 - 2*x^5 - x^6).
|
|
1
|
|
|
|
1, 5, 16, 41, 101, 254, 638, 1609, 4048, 10185, 25631, 64502, 162319, 408476, 1027931, 2586793, 6509675, 16381622, 41224415, 103741401, 261065639, 656972695, 1653274340, 4160471302, 10469842201, 26347398589, 66303330946
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,2
|
|
|
COMMENTS
|
The value of a(0) is undefined. The A(x) leads to a(0)=1, the a(n) formula to a(0)=0 and the recurrence relation to a(0)=6 as pointed out by Bruno Berselli. - Johannes W. Meijer, Jul 10 2011
|
|
|
LINKS
|
|
|
|
FORMULA
|
a(n) = n*Sum_{m=1..n} Sum_{k=m..n} binomial(m, k-m)*Sum_{j=0..k} binomial(k,j) * binomial(j, n-3*k+2*j)))/m).
a(n) = a(n-1) + 2*a(n-2) + 3*a(n-3) + 3*a(n-4) + 2*a(n-5) + a(n-6); a(1)=1, a(2)=5, a(3)=16, a(4)=41, a(5)=101, a(6)=254. - Harvey P. Dale, Jun 14 2011
|
|
|
MAPLE
|
A187004 := proc(n) local m, k, j: (n*add(add(binomial(m, k-m)*add(binomial(k, j)*binomial(j, n-3*k+2*j), j=0..k), k=m..n)/m, m= 1..n)) end: seq(A187004(n), n=1..27); # Johannes W. Meijer, Jul 10 2011
|
|
|
MATHEMATICA
|
LinearRecurrence[{1, 2, 3, 3, 2, 1}, {1, 5, 16, 41, 101, 254}, 30] (* or *) Rest[ CoefficientList[Series[(1+2x^2+6x^3+9x^4+8x^5+5x^6)/(1-x-2x^2- 3x^3-3x^4-2x^5-x^6), {x, 1, 30}], x]] (* Harvey P. Dale, Jun 14 2011 *)
|
|
|
PROG
|
(Maxima) a(n):=n*sum(sum(binomial(m, k-m)*sum(binomial(k, j)*binomial(j, n-3*k+2*j), j, 0, k), k, m, n)/m, m, 1, n);
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
nonn,easy
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
