A257601 a(n) = (n^4 + 20*n^3 + 125*n^2 + 250*n + 24)/12.

2, 35, 100, 210, 380, 627, 970, 1430, 2030, 2795, 3752, 4930, 6360, 8075, 10110, 12502, 15290, 18515, 22220, 26450, 31252, 36675, 42770, 49590, 57190, 65627, 74960, 85250, 96560, 108955, 122502, 137270, 153330, 170755, 189620, 210002, 231980, 255635, 281050, 308310, 337502

Offset

0,1

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Yang-Hui He and John McKay, Sporadic and Exceptional, arXiv:1505.06742 [math.AG], 2015.

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Formula

G.f.: (2 + 25*x - 55*x^2 + 40*x^3 - 10*x^4)/(1-x)^5. - Vincenzo Librandi, Jun 08 2015

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5). - Vincenzo Librandi, Jun 08 2015

E.g.f.: (1/12)*(24 + 396*x + 192*x^2 + 26*x^3 + x^4)*exp(x). - G. C. Greubel, Mar 24 2022

Mathematica

Table[(n^4 +20*n^3 +125*n^2 +250*n +24)/12, {n, 0, 50] (* Bruno Berselli, Jun 08 2015 *)
LinearRecurrence[{5, -10, 10, -5, 1}, {2, 35, 100, 210, 380}, 50] (* Harvey P. Dale, Oct 21 2018 *)

Prog

(Sage) [(n^4 +20*n^3 +125*n^2 +250*n +24)/12 for n in (0..50)] # Bruno Berselli, Jun 08 2015
(Magma) I:=[2, 35, 100, 210, 380]; [n le 5 select I[n] else 5*Self(n-1)-10*Self(n-2)+10*Self(n-3)-5*Self(n-4)+Self(n-5): n in [1..45]]; // Vincenzo Librandi, Jun 08 2015

Crossrefs

Agrees with A257600 except for first term.

Sequence in context: A291162 A042459 A276713 * A282727 A042353 A193576

Adjacent sequences: A257598 A257599 A257600 * A257602 A257603 A257604

Keyword

nonn,easy

Author

N. J. A. Sloane, Jun 07 2015

Status

approved