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!)
A144405 Triangle T(n,k) = binomial(n, k)*(3*binomial(n, k)^2 - binomial(n, k) - 1), read by rows. 2
1, 1, 1, 1, 18, 1, 1, 69, 69, 1, 1, 172, 606, 172, 1, 1, 345, 2890, 2890, 345, 1, 1, 606, 9885, 23580, 9885, 606, 1, 1, 973, 27321, 127365, 127365, 27321, 973, 1, 1, 1464, 65044, 523656, 1024030, 523656, 65044, 1464, 1, 1, 2097, 138636, 1770972, 5985126, 5985126, 1770972, 138636, 2097, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

G. C. Greubel, Rows n = 0..50 of the triangle, flattened

FORMULA

T(n,k) = binomial(n, k)*(3*binomial(n, k)^2 - binomial(n, k) - 1).

Sum_{k=0..n} T(n, k) = A000172(n) - A000984(n) - 2^n = Hypergeometric3F2([-n, -n, -n], [1, 1], -1) - binomial(2*n, n) - 2^n. - G. C. Greubel, Mar 27 2021

EXAMPLE

Triangle begins as:

  1;

  1,    1;

  1,   18,      1;

  1,   69,     69,       1;

  1,  172,    606,     172,        1;

  1,  345,   2890,    2890,      345,        1;

  1,  606,   9885,   23580,     9885,      606,        1;

  1,  973,  27321,  127365,   127365,    27321,      973,       1;

  1, 1464,  65044,  523656,  1024030,   523656,    65044,    1464,      1;

  1, 2097, 138636, 1770972,  5985126,  5985126,  1770972,  138636,   2097,    1;

  1, 2890, 271305, 5169480, 27738690, 47945268, 27738690, 5169480, 271305, 2890, 1;

MAPLE

A144405:= (n, k) -> binomial(n, k)*(3*binomial(n, k)^2 - binomial(n, k) - 1);

seq(seq( A144405(n, k), k=0..n), n=0..12); # G. C. Greubel, Mar 27 2021

MATHEMATICA

Table[Table[Binomial[n, m]*(3*Binomial[n, m]^2 - Binomial[n, m] - 1), {m, 0, n}], {n, 0, 10}]; Flatten[%]

PROG

(Magma) [Binomial(n, k)*(3*Binomial(n, k)^2 - Binomial(n, k) - 1): k in [0..n], n in [0..12]]; // G. C. Greubel, Mar 27 2021

(Sage) flatten([[binomial(n, k)*(3*binomial(n, k)^2 - binomial(n, k) - 1) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Mar 27 2021

CROSSREFS

Cf. A000172, A000984, A144404.

Sequence in context: A168623 A146774 A174451 * A202671 A203004 A155497

Adjacent sequences:  A144402 A144403 A144404 * A144406 A144407 A144408

KEYWORD

nonn,tabl

AUTHOR

Roger L. Bagula and Gary W. Adamson, Oct 03 2008

EXTENSIONS

Edited by G. C. Greubel, Mar 27 2021

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 July 31 20:24 EDT 2021. Contains 346377 sequences. (Running on oeis4.)