OFFSET
0,3
COMMENTS
Binomial transform of [1, 8, 21, 22, 8, 0, 0, 0, ...]. - Gary W. Adamson, Dec 28 2007
For n > 0, a(n) is the n-th antidiagonal sum of the convolution arrays A213752 and A213836). - Clark Kimberling, Jun 20 2012
The first differences are given in A277229, as a convolution of the odd-indexed triangular numbers A000217(2*n+1) and the squares A000290(n), n >= 0. - J. M. Bergot, Sep 14 2016
REFERENCES
T. A. Gulliver, Sequences from Arrays of Integers, Int. Math. Journal, Vol. 1, No. 4, pp. 323-332, 2002.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..2000
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
FORMULA
G.f.: x*(1+x)*(1+3*x)/(1-x)^5. - Colin Barker, Mar 22 2012
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n > 4, a(0)=0, a(1)=1, a(2)=9, a(3)=38, a(4)=110. - Yosu Yurramendi, Sep 03 2013
E.g.f.: (1/6)*x*(6 + 21*x + 14*x^2 + 2*x^3)*exp(x). - G. C. Greubel, Sep 17 2016
MAPLE
MATHEMATICA
Table[n (n + 1) (2 n^2 + 1)/6, {n, 0, 37}] (* or *)
CoefficientList[Series[x (1 + x) (1 + 3 x)/(1 - x)^5, {x, 0, 37}], x] (* Michael De Vlieger, Sep 14 2016 *)
LinearRecurrence[{5, -10, 10, -5, 1}, {0, 1, 9, 38, 110}, 40] (* Harvey P. Dale, Oct 02 2021 *)
PROG
(Magma) [n*(n+1)*(2*n^2+1)/6: n in [0..40]]; // Vincenzo Librandi, Jun 14 2011
(PARI) a(n)=n*(n+1)*(2*n^2+1)/6; \\ Joerg Arndt, Sep 04 2013
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Jun 12 2002
STATUS
approved