login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A136635 Triangle, read by rows, where T(n,k) = C(n,k) * C(2^k*3^(n-k), n) for n>=k>=0. 3
1, 3, 2, 36, 30, 6, 2925, 2448, 660, 56, 1663740, 1265004, 353430, 42504, 1820, 6774333588, 4368213360, 1114691760, 139915440, 8561520, 201376, 204208594169580, 106458751541142, 23004238451040, 2630276490960 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Main diagonal is A014070(n) = C(2^n,n).

Column 0 is A136393(n) = C(3^n,n).

Row sums form A136637.

Antidiagonal sums form A136638.

LINKS

Table of n, a(n) for n=0..24.

FORMULA

G.f.: A(x,y) = Sum_{n>=0} log(1 + 3^n*x + 2^n*x*y)^n / n!.

EXAMPLE

Triangle begins:

1;

3, 2;

36, 30, 6;

2925, 2448, 660, 56;

1663740, 1265004, 353430, 42504, 1820;

6774333588, 4368213360, 1114691760, 139915440, 8561520, 201376;

204208594169580, 106458751541142, 23004238451040, 2630276490960, 167150463480, 5562289824, 74974368; ...

MATHEMATICA

Flatten[Table[Binomial[n, k]Binomial[2^k 3^(n-k), n], {n, 0, 10}, {k, 0, n}]] (* Harvey P. Dale, Dec 13 2012 *)

PROG

(PARI) {T(n, k)=binomial(n, k)*binomial(2^k*3^(n-k), n)}

(PARI) /* Using g.f.: */ {T(n, k)=polcoeff(polcoeff(sum(i=0, n, log(1+3^i*x+2^i*x*y)^i/i!), n, x), k, y)}

CROSSREFS

Cf. A014070 (main diagonal), A136393 (column 0), A136636 (column 1), A136637 (row sums), A136638 (antidiagonal sums).

Sequence in context: A292158 A303729 A296544 * A062743 A009084 A096057

Adjacent sequences:  A136632 A136633 A136634 * A136636 A136637 A136638

KEYWORD

nonn,tabl

AUTHOR

Vladeta Jovovic and Paul D. Hanna, Jan 15 2008

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 December 15 20:00 EST 2019. Contains 330000 sequences. (Running on oeis4.)