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A100430
Bisection of A002417.
1
1, 30, 175, 588, 1485, 3146, 5915, 10200, 16473, 25270, 37191, 52900, 73125, 98658, 130355, 169136, 215985, 271950, 338143, 415740, 505981, 610170, 729675, 865928, 1020425, 1194726, 1390455, 1609300, 1853013, 2123410, 2422371, 2751840
OFFSET
0,2
FORMULA
a(n) = (8*n^4 +28*n^3 +34*n^2 +17*n+3)/3. - Ralf Stephan, May 15 2007
From G. C. Greubel, Apr 09 2023: (Start)
a(n) = (2*n+1)*binomial(2*n+3, 3).
a(n) = (2*n+1)*A000447(n+1).
G.f.: (1 + 25*x + 35*x^2 + 3*x^3)/(1-x)^5.
E.g.f.: (1/3)*(3 + 87*x + 174*x^2 + 76*x^3 + 8*x^4)*exp(x). (End)
MATHEMATICA
Table[(2*n+1)*Binomial[2*n+3, 3], {n, 0, 50}] (* G. C. Greubel, Apr 09 2023 *)
PROG
(Magma) [(2*n+1)*Binomial(2*n+3, 3): n in [0..50]]; // G. C. Greubel, Apr 09 2023
(SageMath) [(2*n+1)*binomial(2*n+3, 3) for n in range(51)] # 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