OFFSET
0,2
REFERENCES
Shigeichi Moriguchi, Kanehisa Udagawa, Shin Hitotsumatsu, "Mathematics Formulas II", Iwanami Shoten, Publishers (1957), p. 14.
LINKS
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
FORMULA
a(n) = n * (2*n+1) * (4*n^2+6*n-1)/3.
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n > 4.
G.f.: x * (9 + 45*x + 11*x^2 - x^3)/(1 - x)^5.
E.g.f.: exp(x)*x*(27 + 108*x + 64*x^2 + 8*x^3)/3. - Stefano Spezia, Nov 10 2024
MATHEMATICA
LinearRecurrence[{5, -10, 10, -5, 1}, {0, 9, 90, 371, 1044}, 35] (* James C. McMahon, Nov 10 2024 *)
PROG
(PARI) a(n) = n*(2*n+1)*(4*n^2+6*n-1)/3;
(PARI) my(N=40, x='x+O('x^N)); concat(0, Vec(x*(9+45*x+11*x^2-x^3)/(1-x)^5))
(Python)
def A377858(n): return n*(n*(n*(n+2<<3)+4)-1)//3 # Chai Wah Wu, Nov 10 2024
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Nov 09 2024
STATUS
approved