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A157411 a(n) = 30*n^4 - 120*n^3 + 120*n^2 - 19. 4
-19, 11, -19, 251, 1901, 6731, 17261, 36731, 69101, 119051, 191981, 294011, 431981, 613451, 846701, 1140731, 1505261, 1950731, 2488301, 3129851, 3887981, 4776011, 5807981, 6998651, 8363501, 9918731, 11681261, 13668731, 15899501, 18392651 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

These are the numerators in column j=4 of the array in A140825 (reference p. 36).

The other columns in A140825 are represented by A000012, A005408, A140811 and A141530.

The link between these columns is given by the first differences: a(n+1) - a(n) = 30*A141530(n), where 30 = A027760(4) = A027760(3) = A027642(4) = A002445(2), then for j=3, A141530(n+1) - A141530(n) = A140070(2)*A140811(n).

REFERENCES

P. Curtz, Integration numerique des systemes differentiels a conditions initiales, Centre de Calcul Scientifique de l'Armement, Note 12, Arcueil (1969).

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

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

FORMULA

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

G.f.: (-19 + 106*x - 264*x^2 + 646*x^3 + 251*x^4)/(1-x)^5.

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) + 720. Fourth differences are constant, 720.

MATHEMATICA

Table[30n^4-120n^3+120n^2-19, {n, 0, 40}] (* or *) LinearRecurrence[{5, -10, 10, -5, 1}, {-19, 11, -19, 251, 1901}, 40] (* Harvey P. Dale, Mar 08 2015 *)

PROG

(MAGMA) [30*n^4 - 120*n^3 + 120*n^2 - 19: n in [0..50]]; // Vincenzo Librandi, Aug 07 2011

(PARI) a(n)=30*n^4-120*n^3+120*n^2-19 \\ Charles R Greathouse IV, Oct 16 2015

CROSSREFS

Sequence in context: A107808 A214422 A141045 * A166525 A083156 A040344

Adjacent sequences:  A157408 A157409 A157410 * A157412 A157413 A157414

KEYWORD

sign,easy

AUTHOR

Paul Curtz, Feb 28 2009

EXTENSIONS

Edited, one index corrected and extended by R. J. Mathar, Sep 17 2009

STATUS

approved

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Last modified February 27 11:28 EST 2020. Contains 332304 sequences. (Running on oeis4.)