A147618 The 3rd Witt transform of A000217.

0, 0, 0, 0, 3, 15, 54, 165, 429, 999, 2145, 4290, 8100, 14586, 25194, 41985, 67830, 106590, 163431, 245157, 360525, 520749, 740025, 1036035, 1430703, 1950975, 2629575, 3506085, 4628052, 6052068, 7845255, 10086780, 12869340, 16301142

Offset

0,5

Comments

The 2nd Witt transform of A000217 is essentially in A032092.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Pieter Moree, The formal series Witt transform, Discr. Math. no. 295 vol. 1-3 (2005) 143-160.

Index entries for linear recurrences with constant coefficients, signature (6,-15,23,-33,51,-64,63,-63,64,-51,33,-23,15,-6,1).

Formula

G.f.: 3*x^4*(1-x+3*x^2-x^3+x^4)/((1-x)^9*(1+x+x^2)^3).

a(n) = (1/81)*(n*(n+3)*(3*n^6 +27*n^5 +45*n^4 -135*n^3 -288*n^2 +108*n -2000)/4480 +2*A049347(n) +A049347(n-1) +(-1)^n*(A099254(n) -2*A099254(n- 1)) -3*(-1)^n*(A128504(n) -2*A128504(n-1))). - G. C. Greubel, Oct 24 2022

Mathematica

CoefficientList[Series[3*x^4*(1-x+3*x^2-x^3+x^4)/((1-x)^9*(1+x+x^2)^3), {x, 0, 40}], x] (* Vincenzo Librandi, Dec 13 2012 *)

Prog

(Magma) R<x>:=PowerSeriesRing(Integers(), 30); [0, 0, 0, 0] cat Coefficients(R!( 3*x^4*(1-x+3*x^2-x^3+x^4)/((1-x)^9*(1+x+x^2)^3) )); // G. C. Greubel, Oct 24 2022
(SageMath)
def A147618_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( 3*x^4*(1-x+3*x^2-x^3+x^4)/((1-x)^9*(1+x+x^2)^3) ).list()
A147618_list(30) # G. C. Greubel, Oct 24 2022

Crossrefs

Cf. A000217, A032092, A049347, A099254, A128504.

Sequence in context: A371481 A332375 A298178 * A290764 A286986 A261565

Adjacent sequences: A147615 A147616 A147617 * A147619 A147620 A147621

Keyword

easy,nonn

Author

R. J. Mathar, Nov 08 2008

Status

approved