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

Author

Jamil da SIlva, Oct 11 2010

Keywords

• nonn
• easy

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).

Crossrefs

Bisections: A181342, A181343.

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