OFFSET
0,2
COMMENTS
Partial sums of A007586.
REFERENCES
A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.
Murray R. Spiegel, Calculus of Finite Differences and Difference Equations, "Schaum's Outline Series", McGraw-Hill, 1971, pp. 10-20, 79-94.
Herbert John Ryser, Combinatorial Mathematics, "The Carus Mathematical Monographs", No. 14, John Wiley and Sons, 1963, pp. 1-8.
LINKS
FORMULA
a(n) = C(n+3, 3)*(9*n+4)/4.
G.f.: (1+8*x)/(1-x)^5.
a(0)=1, a(1)=13, a(2)=55, a(3)=155, a(4)=350, a(n)=5*a(n-1)- 10*a(n-2)+ 10*a(n-3)-5*a(n-4)+a(n-5). - Harvey P. Dale, Aug 19 2012
a(n) = A080852(9,n). - R. J. Mathar, Jul 28 2016
MATHEMATICA
Table[(n+1)(n+2)(n+3)(9n+4)/24, {n, 0, 40}] (* or *) LinearRecurrence[ {5, -10, 10, -5, 1}, {1, 13, 55, 155, 350}, 40] (* Harvey P. Dale, Aug 19 2012 *)
PROG
(Magma) /* A000027 convolved with A051682 (excluding 0): */ A051682:=func<n | n*(9*n-7)/2>; [&+[(n-i+1)*A051682(i): i in [1..n]]: n in [1..35]]; // Bruno Berselli, Dec 07 2012
(PARI) a(n)=(n+1)*(n+2)*(n+3)*(9*n+4)/24 \\ Charles R Greathouse IV, Oct 07 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Barry E. Williams, Dec 11 1999
STATUS
approved