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A257890
Expansion of the g.f. (x^2-x+1)*(x^2-3*x+3)/(x-1)^6.
3
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
Kyu-Hwan Lee, Se-jin Oh, Catalan triangle numbers and binomial coefficients, arXiv:1601.06685 [math.CO], 2016.
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
KEYWORD
nonn,easy
AUTHOR
R. J. Mathar, May 12 2015
STATUS
approved