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A172075 a(n) = n*(n+1)*(9*n^2 - n - 5)/6. 1
0, 1, 29, 146, 450, 1075, 2191, 4004, 6756, 10725, 16225, 23606, 33254, 45591, 61075, 80200, 103496, 131529, 164901, 204250, 250250, 303611, 365079, 435436, 515500, 606125, 708201, 822654, 950446, 1092575, 1250075, 1424016, 1615504, 1825681 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

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

B. Berselli, A description of the recursive method in Formula 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 + 24*x + 11*x^2)/(1-x)^5.

a(n) = n*A172073(n)- Sum_{i=0..n-1} A172073(i).

The last formula is the case d=6 in the identity n*(n*(n+1)*(2*d*n -2*d +3)/6) - Sum_{k=0..n-1} k*(k+1)*(2*d*k - 2*d + 3)/6 = n*(n+1)*(3*d*n^2 -d*n + 4*n - 2*d + 2)/12. - Bruno Berselli, Dec 07 2010

E.g.f.: x*(6 + 81*x + 62*x^2 + 9*x^3)*exp(x)/6. - G. C. Greubel, Aug 30 2019

MAPLE

seq(n*(n+1)*(9*n^2 -n -5)/6, n=0..40); # G. C. Greubel, Aug 30 2019

MATHEMATICA

CoefficientList[Series[x(1+24x+11x^2)/(1-x)^5, {x, 0, 40}], x] (* Vincenzo Librandi, Jan 01 2014 *)

LinearRecurrence[{5, -10, 10, -5, 1}, {0, 1, 29, 146, 450}, 40] (* Harvey P. Dale, May 11 2014 *)

PROG

(Magma) [n*(n+1)*(9*n^2-n-5)/6: n in [0..50]]; // Vincenzo Librandi, Jan 01 2014

(PARI) vector(40, n, m=n-1; n*m*(9*m^2 -m -5)/6) \\ G. C. Greubel, Aug 30 2019

(Sage) [n*(n+1)*(9*n^2 -n -5)/6 for n in (0..40)] # G. C. Greubel, Aug 30 2019

(GAP) List([0..40], n-> n*(n+1)*(9*n^2 -n -5)/6); # G. C. Greubel, Aug 30 2019

CROSSREFS

Cf. A172073.

Sequence in context: A123845 A297722 A042642 * A042644 A263126 A221981

Adjacent sequences: A172072 A172073 A172074 * A172076 A172077 A172078

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Jan 25 2010

STATUS

approved

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Last modified December 6 14:43 EST 2022. Contains 358644 sequences. (Running on oeis4.)