A175898 Expansion of (1+3*x+9*x^2+9*x^3+9*x^4+3*x^5+x^6) /( (1+x)^2 * (1-x)^5 ).
1, 6, 26, 76, 186, 386, 726, 1251, 2031, 3126, 4626, 6606, 9176, 12426, 16486, 21461, 27501, 34726, 43306, 53376, 65126, 78706, 94326, 112151, 132411, 155286, 181026, 209826, 241956, 277626, 317126, 360681, 408601, 461126, 518586, 581236, 649426, 723426
Offset: 0
Links
- Harvey P. Dale, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (3,-1,-5,5,1,-3,1).
Programs
-
Mathematica
LinearRecurrence[{3,-1,-5,5,1,-3,1},{1,6,26,76,186,386,726},40] (* Harvey P. Dale, Feb 27 2012 *) -
PARI
Vec((1+3*x+9*x^2+9*x^3+9*x^4+3*x^5+x^6)/((1+x)^2*(1-x)^5)+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012
-
PARI
a(n)=5*n*(7*n^3 + 14*n^2 + 44*n + 37 + 3*(-1)^n)\/96 + 1 \\ Charles R Greathouse IV, Jul 06 2017
Formula
a(n) = 55*n^2/24 +185*n/96 +59/64 +35*n^4/96 +35*n^3/48 +(5*n/32+5/64)*(-1)^n.
a(2n) = (55*n^2+25*n+6+35*n^4+35*n^3)/6.
a(n) = +3*a(n-1) -a(n-2) -5*a(n-3) +5*a(n-4) +a(n-5) -3*a(n-6) +a(n-7).
Extensions
Edited by R. J. Mathar, Oct 12 2010