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Search: id:A136635
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| A136635 |
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Triangle, read by rows, where T(n,k) = C(n,k) * C(2^k*3^(n-k), n) for n>=k>=0. |
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+0
4
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| 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; listen)
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OFFSET
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0,2
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COMMENT
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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.
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FORMULA
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G.f.: A(x,y) = Sum_{n>=0} log(1 + 3^n*x + 2^n*x*y)^n / n!.
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EXAMPLE
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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; ...
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PROGRAM
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(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)}
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CROSSREFS
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Cf. A014070 (main diagonal), A136393 (column 0), A136636 (column 1), A136637 (row sums), A136638 (antidiagonal sums).
Adjacent sequences: A136632 A136633 A136634 this_sequence A136636 A136637 A136638
Sequence in context: A065353 A046272 A054676 this_sequence A062743 A013324 A009084
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KEYWORD
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nonn,tabl
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AUTHOR
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Vladeta Jovovic (vladeta(AT)Eunet.yu) and Paul D. Hanna (pauldhanna(AT)juno.com), Jan 15 2008
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