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.

Sequence in context: A199629 A098943 A321973 * A247619 A120586 A171373

Adjacent sequences: A178462 A178463 A178464 * A178466 A178467 A178468

Keyword

nonn,changed

Author

Sean A. Irvine, Mar 23 2011

Extensions

Edited by David W. Wilson and R. J. Mathar, Aug 05 2013

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

Status

approved