OFFSET
0,1
COMMENTS
This is the sequence of fourth terms of "second partial sums of m-th powers".
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Luciano Ancora, Demonstration of formulas
Index entries for linear recurrences with constant coefficients, signature (10,-35,50,-24).
FORMULA
G.f.: -2*(77*x^3-100*x^2+40*x-5) / ((x-1)*(2*x-1)*(3*x-1)*(4*x-1)). - Colin Barker, Jan 26 2015
From Peter Bala, Jan 31 2016: (Start)
a(n) = (x + 1)*( Bernoulli(n + 1, x + 1) - Bernoulli(n + 1, 1) )/(n + 1) - ( Bernoulli(n + 2, x + 1) - Bernoulli(n + 2, 1) )/(n + 2) at x = 4.
a(n) = 1/3!*Sum_{k = 0..n} (-1)^(k+n)*(k + 5)!*Stirling2(n,k)/
((k + 1)*(k + 2)). (End)
MAPLE
seq(add(i*(5 - i)^n, i = 1..4), n = 0..20); # Peter Bala, Jan 31 2017
MATHEMATICA
Table[3 2^n + 2^(2 n) + 2 3^n + 4, {n, 0, 25}] (* Bruno Berselli, Jan 27 2015 *)
LinearRecurrence[{10, -35, 50, -24}, {10, 20, 50, 146}, 30] (* Harvey P. Dale, Jun 06 2020 *)
PROG
(PARI) Vec(-2*(77*x^3-100*x^2+40*x-5)/((x-1)*(2*x-1)*(3*x-1)*(4*x-1)) + O(x^100)) \\ Colin Barker, Jan 26 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Luciano Ancora, Jan 26 2015
STATUS
approved