login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A085881 Triangle T(n,k) read by rows: multiply row n of Pascal's triangle (A007318) by A001147(n). 3
1, 1, 1, 3, 6, 3, 15, 45, 45, 15, 105, 420, 630, 420, 105, 945, 4725, 9450, 9450, 4725, 945, 10395, 62370, 155925, 207900, 155925, 62370, 10395, 135135, 945945, 2837835, 4729725, 4729725, 2837835, 945945, 135135, 2027025, 16216200, 56756700, 113513400, 141891750, 113513400, 56756700, 16216200, 2027025 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,4
LINKS
FORMULA
Triangle given by [1, 2, 3, 4, 5, 6, ...] DELTA [1, 2, 3, 4, 5, 6, ...] where DELTA is Deléham's operator defined in A084938.
T(n,k) = A164961(n,k)/2^n. - Philippe Deléham, Jan 07 2012
Recurrence equation: T(n+1,k) = (2*n+1)*(T(n,k) + T(n,k-1)). - Peter Bala, Jul 15 2012
E.g.f.: 1/sqrt(1-2*x-2*x*y). - Peter Bala, Jul 15 2012
G.f.: W(0), where W(k) = 1 - (k+1)*x*(1+y)/( (k+1)*x*(1+y) - 1/W(k+1) ); (continued fraction). - Sergei N. Gladkovskii, Nov 03 2013
EXAMPLE
Triangle starts:
1;
1, 1;
3, 6, 3;
15, 45, 45, 15;
105, 420, 630, 420, 105;
945, 4725, 9450, 9450, 4725, 945;
10395, 62370, 155925, 207900, 155925, 62370, 10395;
135135, 945945, 2837835, 4729725, 4729725, 2837835, 945945, 135135;
...
MAPLE
T:= (n, k)-> n!/2^n*binomial(n, k)*binomial(2*n, n):
seq(seq(T(n, k), k=0..n), n=0..10); # Yu-Sheng Chang, Jan 16 2020
MATHEMATICA
Table[Binomial[n, k]*(2*n-1)!!, {n, 0, 10}, {k, 0, n}]//Flatten (* G. C. Greubel, Feb 07 2020 *)
PROG
(PARI) T(n, k) = binomial(n, k)*binomial(2*n, n)*n!/2^n;
for(n=0, 10, for(k=0, n, print1(T(n, k), ", "))) \\ G. C. Greubel, Feb 07 2020
(Magma) [Binomial(n, k)*Binomial(2*n, n)*Factorial(n)/2^n: k in [0..n], n in [0..10]]; // G. C. Greubel, Feb 07 2020
(Sage) [[binomial(n, k)*(2*n-1).multifactorial(2) for k in (0..n)] for n in (0..10)] # G. C. Greubel, Feb 07 2020
(GAP) Flat(List([0..10], n-> List([0..n], k-> Binomial(n, k)*Binomial(2*n, n) *Factorial(n)/2^n ))); # G. C. Greubel, Feb 07 2020
CROSSREFS
Sequence in context: A205844 A205865 A362585 * A265480 A309084 A288092
KEYWORD
nonn,tabl
AUTHOR
N. J. A. Sloane, Aug 17 2003
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 3 07:04 EDT 2024. Contains 372206 sequences. (Running on oeis4.)