|
Search: id:A047781
|
|
|
| A047781 |
|
Sum(binomial(n-1,k)*binomial(n+k,k),k=0..n-1). Also a(n)=T(n,n), array T as in A049600. |
|
+0
9
|
|
| 0, 1, 4, 19, 96, 501, 2668, 14407, 78592, 432073, 2390004, 13286043, 74160672, 415382397, 2333445468, 13141557519, 74174404608, 419472490257, 2376287945572, 13482186743203, 76598310928096, 435730007006341, 2481447593848524
(list; graph; listen)
|
|
|
OFFSET
|
0,3
|
|
|
COMMENT
|
Also main diagonal of array : m(i,1)=1, m(1,j)=j, m(i,j)=m(i,j-1)+m(i-1,j-1)+m(i-1,j): 1 2 3 4 ... / 1 4 9 16 ... / 1 6 19 44 ... / 1 8 33 96 ... / - Benoit Cloitre (benoit7848c(AT)orange.fr), Aug 05 2002
|
|
REFERENCES
|
G. Rutledge and R. D. Douglass, Integral functions associated with certain binomial coefficient sums, Amer. Math. Monthly, 43 (1936), 27-32.
|
|
LINKS
|
Milan Janjic, Two Enumerative Functions
|
|
FORMULA
|
n*(2*n-3)*a(n)-(12*n^2-24*n+8)*a(n-1)+(2*n-1)*(n-2)*a(n-2) = 0. - Vladeta Jovovic (vladeta(AT)Eunet.yu), Aug 29 2004
Sum k=0..n, binomial(n, k)binomial(n+1, k+1)2^k. - Paul Barry (pbarry(AT)wit.ie), Sep 20 2004
Third binomial transform of A098660. - Paul Barry (pbarry(AT)wit.ie), Sep 20 2004
G.f.: ((1+x)-sqrt(1-6x+x^2))/(4xsqrt(1-6x+x^2)); E.g.f.: exp(3x)(BesselI(0, 2sqrt(x))+BesselI(1, 2sqrt(2)x)/sqrt(2)). - Paul Barry (pbarry(AT)wit.ie), Sep 20 2004
|
|
MAPLE
|
a := proc(n) local k; add(binomial(n-1, k)*binomial(n+k, k), k=0..n-1); end;
|
|
CROSSREFS
|
Cf. A002003.
a(n)=sum(k=0..n T(n, k)), array T as in A008288.
Sequence in context: A027618 A020060 A122394 this_sequence A089354 A083315 A025573
Adjacent sequences: A047778 A047779 A047780 this_sequence A047782 A047783 A047784
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
njas
|
|
|
Search completed in 0.002 seconds
|
