A167555 The third left hand column of triangle A167552.

2, 14, 63, 209, 559, 1281, 2618, 4902, 8568, 14168, 22385, 34047, 50141, 71827, 100452, 137564, 184926, 244530, 318611, 409661, 520443, 654005, 813694, 1003170, 1226420, 1487772, 1791909, 2143883, 2549129, 3013479, 3543176

Offset

3,1

Links

G. C. Greubel, Table of n, a(n) for n = 3..1002

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

Formula

a(n) = (14*n^5 - 115*n^4 + 400*n^3 - 665*n^2 + 486*n - 120)/5!.

G.f.: (z^3 + 9*z^2 + 2*z + 2)/(z-1)^6.

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).

a(n) - 5*a(n-1) + 10*a(n-2) - 10*a(n-3) + 5*a(n-4) - a(n-5) = 2*7.

Mathematica

LinearRecurrence[{6, -15, 20, -15, 6, -1}, {2, 14, 63, 209, 559, 1281}, 40] (* or *) Table[1/120*(66*n+95*n^2+40*n^3+25*n^4+14*n^5), {n, 40}] (* Harvey P. Dale, Mar 26 2012 *)

Crossrefs

Equals the third left hand column of triangle A167552.

Other left hand columns are A005408, A167554, A168302 and A168303.

Sequence in context: A217154 A144657 A362157 * A222445 A181394 A335630

Adjacent sequences: A167552 A167553 A167554 * A167556 A167557 A167558

Keyword

easy,nonn

Author

Johannes W. Meijer, Nov 10 2009

Status

approved