OFFSET
0,2
REFERENCES
G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976, p. 190.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).
FORMULA
a(n) = A008780(n) - binomial(n, 4) - binomial(n, 3).
G.f.: (x^4 - 3*x^3 - 3*x^2 + 5*x + 1)/(x-1)^6. - Colin Barker, Jul 22 2012
a(n) = (n+1)*(n+4)*(n^3 + 40*n^2 + 61*n + 30)/120. - Robert Israel, Jul 06 2016
MAPLE
a:= n-> 1+10*n+27*binomial(n, 2)+28*binomial(n, 3)
+11*binomial(n, 4)+binomial(n, 5):
seq(a(n), n=0..34);
MATHEMATICA
LinearRecurrence[{6, -15, 20, -15, 6, -1}, {1, 11, 48, 140, 326, 657}, 40] (* Harvey P. Dale, Jan 27 2013 *)
CoefficientList[Series[(x^4 -3x^3 -3x^2 +5x +1)/(x-1)^6, {x, 0, 40}], x] (* Vincenzo Librandi, Oct 27 2013 *)
PROG
(Magma) [1 + 10*n + 27*Binomial(n, 2) + 28*Binomial(n, 3) + 11*Binomial(n, 4) + Binomial(n, 5): n in [0..40]]; // Vincenzo Librandi, Oct 27 2013
(PARI) my(x='x+O('x^40)); Vec((x^4-3*x^3-3*x^2+5*x+1)/(x-1)^6) \\ G. C. Greubel, Feb 17 2019
(Sage) ((x^4-3*x^3-3*x^2+5*x+1)/(x-1)^6).series(x, 40).coefficients(x, sparse=False) # G. C. Greubel, Feb 17 2019
(GAP) List([0..40], n->(n+1)*(n+4)*(n^3+40*n^2+61*n+30)/120); # Muniru A Asiru, Feb 17 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Alford Arnold, Aug 15 1998
EXTENSIONS
More terms from Erich Friedman
STATUS
approved