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A100431
Bisection of A002417.
4
8, 80, 336, 960, 2200, 4368, 7840, 13056, 20520, 30800, 44528, 62400, 85176, 113680, 148800, 191488, 242760, 303696, 375440, 459200, 556248, 667920, 795616, 940800, 1105000, 1289808, 1496880, 1727936, 1984760, 2269200, 2583168, 2928640, 3307656, 3722320
OFFSET
0,1
FORMULA
a(n) = (4/3)*(2*n^4 + 11*n^3 + 22*n^2 + 19*n + 6). - Ralf Stephan, May 15 2007
G.f.: 8*(1 + 5*x + 2*x^2)/(1 - x)^5. - Ilya Gutkovskiy, Feb 24 2017
From G. C. Greubel, Apr 09 2023: (Start)
a(n) = (8/3)*binomial(n+2, 2)*binomial(2*n+3, 2).
a(n) = (8/3)*A000217(n+1)*A014105(n+1).
a(n) = 8*A108678(n).
a(n) = 4*A098077(n+1).
E.g.f.: (4/3)*(6 + 54*x + 69*x^2 + 23*x^3 + 2*x^4)*exp(x). (End)
MATHEMATICA
Table[4*(n+1)^2(n+2)(2n+3)/3, {n, 0, 60}] (* Vladimir Joseph Stephan Orlovsky, Jul 07 2011 *)
PROG
(Magma) [4*(n+1)^2*(n+2)*(2*n+3)/3: n in [0..60]]; // G. C. Greubel, Apr 09 2023
(SageMath) [4*(n+1)^2*(n+2)*(2*n+3)/3 for n in range(61)] # G. C. Greubel, Apr 09 2023
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Nov 20 2004
EXTENSIONS
More terms from Hugo Pfoertner, Nov 26 2004
STATUS
approved