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Search: id:A105477
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| A105477 |
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Triangle read by rows: T(n,k) is the number of compositions of n into k parts when there are two kinds of part 2. |
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+0
2
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| 1, 2, 1, 1, 4, 1, 1, 6, 6, 1, 1, 6, 15, 8, 1, 1, 7, 23, 28, 10, 1, 1, 8, 30, 60, 45, 12, 1, 1, 9, 39, 98, 125, 66, 14, 1, 1, 10, 49, 144, 255, 226, 91, 16, 1, 1, 11, 60, 202, 437, 561, 371, 120, 18, 1, 1, 12, 72, 272, 685, 1128, 1092, 568, 153, 20, 1, 1, 13, 85, 355, 1015, 1995, 2555
(list; table; graph; listen)
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OFFSET
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1,2
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FORMULA
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G.f.=tz(1+z-z^2)/(1-z-tz-tz^2+tz^3).
T(n,k)=Sum(binomial(k,j)*binomial(n-2j-1, k-j-1), j=0..n-k). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 06 2006
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EXAMPLE
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T(4,2)=6 because we have (1,3),(3,1),(2,2),(2,2'),(2',2) and (2',2').
Triangle begins:
1;
2,1;
1,4,1;
1,6,6,1;
1,6,15,8,1;
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MAPLE
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G:=t*z*(1+z-z^2)/(1-z-t*z-t*z^2+t*z^3): Gser:=simplify(series(G, z=0, 15)): for n from 1 to 14 do P[n]:=coeff(Gser, z^n) od: for n from 1 to 13 do seq(coeff(P[n], t^k), k=1..n) od; # yields sequence in triangular form
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CROSSREFS
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Row sums yield A077998.
Sequence in context: A061462 A122578 A005131 this_sequence A127709 A131350 A131087
Adjacent sequences: A105474 A105475 A105476 this_sequence A105478 A105479 A105480
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KEYWORD
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nonn,tabl
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 09 2005
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