A187695 G.f.: x^4*(1+x)*(1+12*x-31*x^2+12*x^2)/((1-x)^2*(1-2*x)^2*(1-3*x)*(1-4*x)).

0, 0, 0, 0, 1, 26, 264, 1846, 10616, 54354, 258388, 1168862, 5109696, 21805162, 91460972, 378874998, 1555269016, 6341845250, 25732834116, 104034429454, 419461348976, 1687846763418, 6781455643420, 27216164395430, 109135969307976, 437358413244466, 1751878519306484, 7014851306040126, 28081422396752416

Offset

0,6

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

F. Bergeron, M. Bousquet-Mélou and S. Dulucq, Standard paths in the composition poset, Ann. Sci. Math. Quebec, 19 (1995), no. 2, 139-151.

Index entries for linear recurrences with constant coefficients, signature (13,-67,175,-244,172,-48).

Formula

a(n) = 27*2^(n-4)*n + 33*2^(n-4) - 2*n + 2 - 26*3^(n-2)+25*4^(n-3), n>1. - R. J. Mathar, Mar 17 2011

E.g.f.: (-901 -228*x + 1152*(1-x)*exp(x) + (1188 + 1944*x)*exp(2*x) - 1664*exp(3*x) + 225*exp(4*x))/576. - G. C. Greubel, Nov 06 2018

Mathematica

Join[{0, 0}, LinearRecurrence[{13, -67, 175, -244, 172, -48}, {0, 0, 1, 26, 264, 1846}, 30]] (* Harvey P. Dale, Mar 02 2015 *)

Prog

(Maxima) makelist(coeff(taylor(x^4*(1+x)*(1+12*x-31*x^2+12*x^2)/((1-x)^2*(1-2*x)^2*(1-3*x)*(1-4*x)), x, 0, n), x, n), n, 0, 28); /* Bruno Berselli, May 30 2011 */
(Magma) [0, 0] cat [27*2^(n-4)*n +33*2^(n-4)-2*n+2-26*3^(n-2)+25*4^(n-3): n in [2..30]]; // Vincenzo Librandi, Feb 19 2012
(PARI) concat([0, 0], vector(30, n, n++; 27*2^(n-4)*n +33*2^(n-4)-2*n+2-26*3^(n-2)+25*4^(n-3))) \\ G. C. Greubel, Nov 06 2018

Crossrefs

Cf. A187693.

Sequence in context: A016106 A200041 A092723 * A328874 A195755 A186261

Adjacent sequences: A187692 A187693 A187694 * A187696 A187697 A187698

Keyword

nonn

Author

N. J. A. Sloane, Mar 12 2011

Status

approved