OFFSET
0,2
LINKS
OEIS Wiki, Figurate numbers
Eric Weisstein's World of Mathematics, Heptagonal Number
Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1)
FORMULA
O.g.f.: (1 + 4*x)^2/(1 - x)^6.
E.g.f.: (24 + 312*x + 696*x^2 + 424*x^3 + 85*x^4 + 5*x^5)*exp(x)/24.
a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6).
a(n) = (n + 1)*(n + 2)*(n + 3)*(5*n^2 + 5*n + 4)/24.
MATHEMATICA
LinearRecurrence[{6, -15, 20, -15, 6, -1}, {1, 14, 85, 320, 910, 2156}, 36]
Table[(n + 1) (n + 2) (n + 3) ((5 n^2 + 5 n + 4)/24), {n, 0, 35}]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Ilya Gutkovskiy, Apr 20 2016
STATUS
approved