OFFSET
0,2
COMMENTS
For a combinatorial interpretation following from the g.f. and the a(n) = h^{(5)}_n formula below see A039755.
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (25,-230,950,-1689,945).
FORMULA
a(n) = A039755(n+4,4), n >= 0.
G.f.: 1/Product_{j=0..4}(1 - (1+2*j)*x).
E.g.f.: (d^4/dx^4)(exp(x)*((exp(2*x)-1)/2)^4/4!) = (2187/128)*exp(9*x) - (2401/96)*exp(7*x) + (625/64)*exp(5*x) - (27/32)*exp(3*x) + (1/384)*exp(x).
a(n) = h^{(5)}_n, the complete homogeneous symmetric function of degree n of the five symbols 1, 3, 5, 7, 9.
From Colin Barker, Dec 23 2017: (Start)
G.f.: 1 / ((1 - x)*(1 - 3*x)*(1 - 5*x)*(1 - 7*x)*(1 - 9*x)).
a(n) = (1 - 4*3^(4+n) + 6*5^(4+n) - 4*7^(4+n) + 9^(4+n)) / 384.
a(n) = 25*a(n-1) - 230*a(n-2) + 950*a(n-3) - 1689*a(n-4) + 945*a(n-5) for n>4.
(End)
EXAMPLE
a(2) = h^{(5)}_2 = 1^2 + 3^2 + 5^2 + 7^2 + 9^2 + 1^1*(3^1 + 5^1 + 7^1 + 9^1) + 3^1*(5^1 + 7^1 + 9^1) + 5^1*(7^1 + 9^1) + 7^1*9^1 = 165 + 230 = 395. The multichoose(5, 2) = binomial(6, 2) = 15 polytopes are five squares and ten rectangles of total area 165 and 230, respectively.
PROG
(PARI) Vec(1 / ((1 - x)*(1 - 3*x)*(1 - 5*x)*(1 - 7*x)*(1 - 9*x)) + O(x^40)) \\ Colin Barker, Dec 23 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, May 26 2017
STATUS
approved