A178465 Expansion of -2*x^2*(-3-2*x+x^2-x^3-2*x^4+x^5) / ( (1+x)^2*(x-1)^4 ).

0, 0, 6, 16, 36, 66, 114, 176, 264, 370, 510, 672, 876, 1106, 1386, 1696, 2064, 2466, 2934, 3440, 4020, 4642, 5346, 6096, 6936, 7826, 8814, 9856, 11004, 12210, 13530, 14912, 16416, 17986, 19686, 21456, 23364, 25346, 27474, 29680, 32040, 34482

Offset

0,3

Links

Table of n, a(n) for n=0..41.

Formula

For n even, a(n) = n*(2+n^2)/2 = A061804(n/2). For n>1 and odd, a(n)=(n+1)*(n^2-n+2)/2 = 2*A212133((n+1)/2).

a(n) = (2-2*(-1)^n+(3+(-1)^n)*n+2*n^3)/4 for n>1. [Colin Barker, Feb 18 2013]

Mathematica

CoefficientList[ Series[ 2x^2 (3 + 2x - x^2 + x^3 + 2x^4 - x^5)/((1 + x)^2 (x - 1)^4), {x, 0, 42}], x] (* Robert G. Wilson v, Feb 17 2014 *)

Prog

(Python)
def A178465(n): return n+(m:=n&1)+(n*(n**2-m)>>1) if n != 1 else 0 # Chai Wah Wu, Aug 30 2022

Crossrefs

Cf. A187062, A187397, A061804, A018808.

Sequence in context: A199629 A098943 A321973 * A247619 A120586 A171373

Adjacent sequences: A178462 A178463 A178464 * A178466 A178467 A178468

Keyword

nonn

Author

Sean A. Irvine, Mar 23 2011

Extensions

Discrepancy with A018808 resolved. David W. Wilson, Aug 05 2013

First line of formulas corrected. R. J. Mathar, Aug 05 2013

Prepended a(0)=0, Joerg Arndt, Feb 19 2014

Status

approved