A212330 Expansion of x^5*(1 - x)^2*(4 - 14*x + 8*x^2 + 11*x^3 - 6*x^4 - 2*x^5 + 2*x^6 + 5*x^7 - 2*x^8 + x^9)/(1 - 2*x)^4.

0, 0, 0, 0, 0, 4, 10, 24, 61, 148, 349, 808, 1847, 4174, 9346, 20764, 45825, 100552, 219528, 477152, 1033008, 2228480, 4792064, 10274816, 21972224, 46872576, 99768320, 211918848, 449277952, 950796288, 2008809472, 4237557760, 8926068736, 18776326144

Offset

0,6

Links

Bruno Berselli, Table of n, a(n) for n = 0..1000

Toufik Mansour, Sherry H. F. Yan and Laura L. M. Yang, Counting occurrences of 231 in an involution, Discrete Mathematics 306 (2006), pages 564-572 (see Corollary 3.5, first case).

Index entries for linear recurrences with constant coefficients, signature (8,-24,32,-16).

Formula

G.f.: x^5*(1-x)^2*(4-14*x+8*x^2+11*x^3-6*x^4-2*x^5+2*x^6+5*x^7-2*x^8+x^9)/(1-2*x)^4.

For n>12, a(n) = 2^(n-17)*(n^3+414*n^2+12227*n-30762)/3.

a(n) = 8*a(n-1)-24*a(n-2)+32*a(n-3)-16*a(n-4) for n>16, n=4, n=11.

Mathematica

CoefficientList[Series[x^5 (1 - x)^2 (4 - 14 x + 8 x^2 + 11 x^3 - 6 x^4 - 2 x^5 + 2 x^6 + 5 x^7 - 2 x^8 + x^9)/(1 - 2 x)^4, {x, 0, 34}], x]

Prog

(PARI) Vec(x^5*(1-x)^2*(4-14*x+8*x^2+11*x^3-6*x^4-2*x^5+2*x^6+5*x^7-2*x^8+x^9)/(1-2*x)^4+O(x^34)) \\ show terms starting with 4.
(Maxima) makelist(coeff(taylor(x^5*(1-x)^2*(4-14*x+8*x^2+11*x^3-6*x^4-2*x^5+2*x^6+5*x^7-2*x^8+x^9)/(1-2*x)^4, x, 0, n), x, n), n, 0, 33);

Crossrefs

Cf. A192886.

Sequence in context: A225127 A230954 A190169 * A291412 A366645 A001868

Adjacent sequences: A212327 A212328 A212329 * A212331 A212332 A212333

Keyword

nonn,easy

Author

Bruno Berselli, May 28 2012

Status

approved