A058796 Row 5 of A007754.

33, 492, 2055, 5898, 13797, 28248, 52587, 91110, 149193, 233412, 351663, 513282, 729165, 1011888, 1375827, 1837278, 2414577, 3128220, 4000983, 5058042, 6327093, 7838472, 9625275, 11723478, 14172057, 17013108, 20291967, 24057330

Offset: 0

Author

Christian G. Bower, Dec 02 2000

Keywords

• nonn
• easy

Comments

a(n) is divisible by n+3.

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Crossrefs

Cf. A007754.

Programs

GAP

List([0..40], n -> 33+173*n+189*n^2+81*n^3+15*n^4+n^5); # G. C. Greubel, Nov 29 2018

Magma

[33+173*n+189*n^2+81*n^3+15*n^4+n^5: n in [0..40]]; // Vincenzo Librandi, Sep 22 2016

Maple

seq(coeff(series(3*(6*x^5-37*x^4+96*x^3-134*x^2+98*x+11)/(1-x)^6,x,n+1), x, n), n = 0 .. 30); # Muniru A Asiru, Nov 30 2018

Mathematica

LinearRecurrence[{6, -15, 20, -15, 6, -1}, {33, 492, 2055, 5898, 13797, 28248}, 30] (* Vincenzo Librandi, Sep 22 2016 *)

PARI

vector(40, n, n--; 33 +173*n +189*n^2 +81*n^3 +15*n^4 +n^5) \\ G. C. Greubel, Nov 29 2018

Python

for n in range(0, 40): print(33+173*n+189*n**2+81*n**3+15*n**4+n**5, end=', ') # Stefano Spezia, Nov 30 2018

Sage

[(33 +173*n +189*n^2 +81*n^3 +15*n^4 +n^5) for n in range(40)] # G. C. Greubel, Nov 29 2018

Formula

From Colin Barker, Jan 16 2013: (Start)

a(n) = 33 + 173*n + 189*n^2 + 81*n^3 + 15*n^4 + n^5.

a(n) = (n + 3)*(n^4 + 12*n^3 + 45*n^2 + 54*n + 11).

G.f.: 3*(6*x^5 - 37*x^4 + 96*x^3 - 134*x^2 + 98*x + 11) / (x-1)^6.

(End)

E.g.f.: (33 + 459*x + 552*x^2 + 196*x^3 + 25*x^4 + x^5)*exp(x). - G. C. Greubel, Nov 29 2018