A299074 Expansion of 1/((1-x)*(1-2*x)*(1-6*x)*(1-24*x)).
1, 33, 853, 20853, 502789, 12080901, 290025541, 6961116741, 167069824837, 4009693935429, 96232763288389, 2309586971953989, 55430091245099845, 1330322213391637317, 31927733262454774597, 766265599145247529797, 18390374384563938483013, 441368985260002510461765
Offset: 0
Links
- Colin Barker, Table of n, a(n) for n = 0..700
- Index entries for linear recurrences with constant coefficients, signature (33,-236,492,-288).
Programs
-
PARI
N=66; x='x+O('x^N); Vec(1/prod(k=1, 4, (1-k!*x))) -
PARI
Vec(1/((1 - x)*(1 - 2*x)*(1 - 6*x)*(1 - 24*x)) + O(x^20)) \\ Colin Barker, Feb 02 2018
Formula
O.g.f.: 1/((1 - x)*(1 - 2*x)(1 - 6*x)*(1 - 24*x)).
From Colin Barker, Feb 02 2018: (Start)
a(n) = (-11 + 115*2^n - 759*6^n + 1920*24^n) / 1265.
a(n) = 33*a(n-1) - 236*a(n-2) + 492*a(n-3) - 288*a(n-4) for n>3. (End)