login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A171379 Triangle, read by rows, T(n, k) = A059481(n,k)*(A059481(n,k) - 1)/2. 1
0, 1, 3, 3, 15, 45, 6, 45, 190, 595, 10, 105, 595, 2415, 7875, 15, 210, 1540, 7875, 31626, 106491, 21, 378, 3486, 21945, 106491, 426426, 1471470, 28, 630, 7140, 54285, 313236, 1471470, 5887596, 20701395, 36, 990, 13530, 122265, 827541, 4507503, 20701395, 82812015, 295475895 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Row sums are: {0, 4, 63, 836, 11000, 147757, 2030217, 28435780, 404461170, 5824442504, ...}.

The sequence is the number of connections between figurate numbers A059481 as points page 25 Riordan.

REFERENCES

J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 25.

LINKS

G. C. Greubel, Rows n = 1..100 of triangle, flattened

FORMULA

T(n,k) = binomial(n+k-1, k)*(binomial(n+k-1, k) - 1)/2.

EXAMPLE

Triangle begins as:

   0;

   1,   3;

   3,  15,   45;

   6,  45,  190,   595;

  10, 105,  595,  2415,   7875;

  15, 210, 1540,  7875,  31626,  106491;

  21, 378, 3486, 21945, 106491,  426426, 1471470;

  28, 630, 7140, 54285, 313236, 1471470, 5887596, 20701395;

MAPLE

seq(seq( binomial(binomial(n+k-1, k), 2), k=1..n), n=1..10); # G. C. Greubel, Nov 28 2019

MATHEMATICA

Table[Binomial[Binomial[n+k-1, k], 2], {n, 10}, {k, n}]//Flatten (* modified by G. C. Greubel, Nov 28 2019 *)

PROG

(PARI) T(n, k) = binomial(binomial(n+k-1, k), 2); \\ G. C. Greubel, Nov 28 2019

(MAGMA) [Binomial(Binomial(n+k-1, k), 2): k in [1..n], n in [1..10]]; // G. C. Greubel, Nov 28 2019

(Sage) [[binomial(binomial(n+k-1, k), 2) for k in (1..n)] for n in (1..10)] # G. C. Greubel, Nov 28 2019

(GAP) Flat(List([1..10], n-> List([1..n], k-> Binomial(Binomial(n+k-1, k), 2) ))); # G. C. Greubel, Nov 28 2019

CROSSREFS

Cf. A059481, A143418.

Sequence in context: A126319 A165553 A056314 * A078631 A160639 A280781

Adjacent sequences:  A171376 A171377 A171378 * A171380 A171381 A171382

KEYWORD

nonn,tabl

AUTHOR

Roger L. Bagula, Dec 07 2009

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 6 02:20 EDT 2020. Contains 333267 sequences. (Running on oeis4.)