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A172085 (27n^4 + 22n^3 - 21n^2 - 16n)/12. 1
0, 1, 41, 212, 660, 1585, 3241, 5936, 10032, 15945, 24145, 35156, 49556, 67977, 91105, 119680, 154496, 196401, 246297, 305140, 373940, 453761, 545721, 650992, 770800, 906425, 1059201, 1230516, 1421812, 1634585, 1870385, 2130816, 2417536 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

The sequence is related to A172082 by a(n) = n*A172082(n)-sum(A172082(i), i=0..n-1).

This is the case d=9 in the identity n*(n*(n+1)*(2*d*n-2*d+3)/6)-sum(k*(k+1)*(2*d*k-2*d+3)/6, k=0..n-1) = n*(n+1)*(3*d*n^2-d*n+4*n-2*d+2)/12. - Bruno Berselli, May 07 2010, Jan 28 2011

LINKS

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

B. Berselli, A description of the recursive method in Comments lines: website Matem@ticamente (in Italian).

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

FORMULA

a(n) = n*(n+1)*(27*n^2-5*n-16)/12.

G.f.: x*(1+36*x+17*x^2)/(1-x)^5; a(n)=5*a(n-1)-10*a(n-2)+10*a(n-3)-5*a(n-4)+a(n-5). - Bruno Berselli, Jan 28 2011

MATHEMATICA

CoefficientList[Series[x (1 + 36 x + 17 x^2)/(1 - x)^5, {x, 0, 40}], x] (* Vincenzo Librandi, Jan 02 2014 *)

PROG

(MAGMA) [n*(n+1)*(27*n^2-5*n-16)/12: n in [0..40]]; // Vincenzo Librandi, Jan 02 2014

CROSSREFS

Cf. A172082.

Sequence in context: A142526 A088319 A204620 * A251094 A142392 A142943

Adjacent sequences:  A172082 A172083 A172084 * A172086 A172087 A172088

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Jan 25 2010

EXTENSIONS

Librandi's contribution restored and rewritten from Bruno Berselli, Feb 29 2012

STATUS

approved

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Last modified November 22 15:27 EST 2017. Contains 295089 sequences.