OFFSET
1,1
LINKS
T. D. Noe, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (21,-210,1330,-5985,20349,-54264, 116280,-203490,293930,-352716, 352716,-293930,203490,-116280,54264,-20349,5985, -1330,210,-21,1).
FORMULA
a(n) = T(n,10); T(n,k) = Sum_{i=1..n} binomial(n+1, i)*binomial(k-1, i-1)*binomial(n-i+k, k).
G.f.: 2*x*(x^18 +9*x^17 +81*x^16 +324*x^15 +1296*x^14 +3024*x^13 +7056*x^12 +10584*x^11 +15876*x^10 +15876*x^9 +15876*x^8 +10584*x^7 +7056*x^6 +3024*x^5 +1296*x^4 +324*x^3 +81*x^2 +9*x +1)/(1-x)^21. - Colin Barker, Jan 25 2013
From G. C. Greubel, Jan 24 2022: (Start)
a(n) = (184756/20!)*n*(n+1)*(1316818944000 +2540101939200*n +3742987138560*n^2 +2615609097216*n^3 +1848671853984*n^4 +695217071376*n^5 +310567813984*n^6 +71342133912*n^7 +22639753938*n^8 +3337504857*n^9 +803922153*n^10 +76623228*n^11 +14628472*n^12 +873558*n^13 +136302*n^14 +4644*n^15 +606*n^16 +9*n^17 +n^18).
a(n) = (n+1)*binomial(n+9, 10)*Hypergeometric3F2([-9, -n, 1-n], [2, -n-9], 1). (End)
MATHEMATICA
A103881[n_, k_]:= (n+1)*Binomial[n+k-1, k]*HypergeometricPFQ[{1-n, -n, 1-k}, {2, 1-n-k}, 1];
Table[A157059[n], {n, 50}] (* G. C. Greubel, Jan 24 2022 *)
PROG
(Sage)
def A103881(n, k): return sum( binomial(n+1, i)*binomial(k-1, i-1)*binomial(n-i+k, k) for i in (0..n) )
[A157059(n, 10) for n in (1..50)] # G. C. Greubel, Jan 24 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
R. H. Hardin, Feb 22 2009
STATUS
approved