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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

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Last modified June 17 15:38 EDT 2021. Contains 345085 sequences. (Running on oeis4.)