A100430 Bisection of A002417.

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

Author

N. J. A. Sloane, Nov 20 2004

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Crossrefs

Cf. A000447, A002417, A100431.

Programs

Magma

[(2*n+1)*Binomial(2*n+3,3): n in [0..50]]; // G. C. Greubel, Apr 09 2023

Mathematica

Table[(2*n+1)*Binomial[2*n+3,3], {n,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

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)

Extensions

More terms from Hugo Pfoertner, Nov 26 2004