A257890 Expansion of the g.f. (x^2-x+1)*(x^2-3*x+3)/(x-1)^6.

3, 12, 34, 80, 166, 314, 553, 920, 1461, 2232, 3300, 4744, 6656, 9142, 12323, 16336, 21335, 27492, 34998, 44064, 54922, 67826, 83053, 100904, 121705, 145808, 173592, 205464, 241860, 283246, 330119, 383008, 442475, 509116, 583562, 666480, 758574, 860586

Offset

0,1

Comments

Absolute values of the 5th column of A220074.

Convolution of A000124 and the sequence 3, 6, 10, 15 (the triangular numbers A000217 without the first two entries).

Links

G. C. Greubel, Table of n, a(n) for n = 0..5000

Kyu-Hwan Lee, Se-jin Oh, Catalan triangle numbers and binomial coefficients, arXiv:1601.06685 [math.CO], 2016.

Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Formula

G.f.: (x^2-x+1)*(x^2-3*x+3)/(x-1)^6.

a(n) = A000292(n+1) + (n+1) + A000389(n+5).

a(n) = (n+1)*(n^4 +14*n^3 +91*n^2 +254*n +360)/120.

a(n) = 6*a(n-1)-15*a(n-2)+20*a(n-3)-15*a(n-4)+6*a(n-5)-a(n-6) for n>6. - Wesley Ivan Hurt, Jan 27 2016

E.g.f.: (360 + 1080*x + 780*x^2 + 220*x^3 + 25*x^4 + x^5)*exp(x)/120. - G. C. Greubel, Nov 24 2017

Mathematica

LinearRecurrence[{6, -15, 20, -15, 6, -1}, {3, 12, 34, 80, 166, 314}, 50] (* Vincenzo Librandi, May 12 2015 *)

Prog

(Magma) [(n+1)*(n^4+14*n^3+91*n^2+254*n+360)/120: n in [0..40]]; // Vincenzo Librandi, May 12 2015
(PARI) Vec((x^2-x+1)*(x^2-3*x+3)/(x-1)^6 + O(x^50)) \\ Michel Marcus, Jan 28 2016

Crossrefs

Cf. A000124, A000217, A220074.

Sequence in context: A117655 A081423 A184705 * A060298 A304975 A226546

Adjacent sequences: A257887 A257888 A257889 * A257891 A257892 A257893

Keyword

nonn,easy

Author

R. J. Mathar, May 12 2015

Status

approved