A257600 Expansion of (4 + 15*x - 35*x^2 + 20*x^3 - 2*x^5)/(1 - x)^5.

4, 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

Offset

0,1

Links

Colin Barker, 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

a(n) = (24 + 250*n + 125*n^2 + 20*n^3 + n^4)/12 for n > 0. - Colin Barker, Apr 15 2016

From G. C. Greubel, Mar 24 2022: (Start)

a(n) = 2*[n=0] + A257601(n).

E.g.f.: 2 + (1/12)*(24 + 396*x + 192*x^2 + 26*x^3 + x^4)*exp(x). (End)

Mathematica

CoefficientList[Series[(4 +15x -35x^2 +20x^3 -2x^5)/(1-x)^5, {x, 0, 50}], x] (* Vincenzo Librandi, Jun 08 2015

Prog

(Magma) I:=[4, 35, 100, 210, 380, 627]; [n le 6 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..51]]; // Vincenzo Librandi, Jun 08 2015
(PARI) Vec((4+15*x-35*x^2+20*x^3-2*x^5)/(1-x)^5 + O(x^50)) \\ Colin Barker, Apr 15 2016
(Sage) [2*bool(n==0) + (24+250*n+125*n^2+20*n^3+n^4)/12 for n in (0..50)] # G. C. Greubel, Mar 24 2022

Crossrefs

Agrees with A257601 except for first term.

Sequence in context: A003349 A344642 A297546 * A211612 A068968 A228887

Adjacent sequences: A257597 A257598 A257599 * A257601 A257602 A257603

Keyword

nonn,easy

Author

N. J. A. Sloane, Jun 07 2015

Status

approved