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A172077 n*(n+1)*(7*n^2-n-4)/4. 1
0, 1, 33, 168, 520, 1245, 2541, 4648, 7848, 12465, 18865, 27456, 38688, 53053, 71085, 93360, 120496, 153153, 192033, 237880, 291480, 353661, 425293, 507288, 600600, 706225, 825201, 958608, 1107568, 1273245, 1456845, 1659616, 1882848, 2127873 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

The sequence is related to A172076 by a(n) = n*A172076(n)-sum(A172076(i), i=0..n-1).

This is the case d=7 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, Apr 21 2010

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

G.f. -x*(1+28*x+13*x^2) / (x-1)^5 . - R. J. Mathar, Nov 17 2011

MATHEMATICA

CoefficientList[Series[x (1 + 28 x + 13 x^2)/(1 - x)^5, {x, 0, 40}], x] (* Vincenzo Librandi, Jan 01 2014 *)

PROG

(MAGMA) [n*(n+1)*(7*n^2-n-4)/4: n in [0..50]]; // Vincenzo Librandi, Jan 01 2014

CROSSREFS

Cf. A172076.

Sequence in context: A233064 A183776 A256021 * A180943 A113752 A155883

Adjacent sequences:  A172074 A172075 A172076 * A172078 A172079 A172080

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Jan 25 2010

STATUS

approved

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Last modified March 28 19:06 EDT 2017. Contains 284246 sequences.