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 A105477 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. 2
 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; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Triangle T(n,k), 1<=k<=n, given by (0, 2, -3/2, -1/6, 2/3, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (1, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938. Triangle T(n,k), 0<=k<=n, is the Riordan array (1, x*(1+x-x^2)/(1-x)) . - Philippe Deléham, Jan 25 2012 LINKS FORMULA 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, Aug 06 2006 T(n,k) = T(n-1,k) + T(n-1,k-1) + T(n-2,k-1) - T(n-3,k-1), n>1. - Philippe Deléham, Jan 25 2012 EXAMPLE 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; Triangle T(n,k) given by (0,2,-3/2,-1/6,2/3,0,0,0,...) DELTA (1,0,0,0,0,...) begins : 1 0, 1 0, 2, 1 0, 1, 4, 1 0, 1, 6, 6, 1 0, 1, 6, 15, 8, 1... MAPLE 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 CROSSREFS Row sums yield A077998. Diagonals : A000012, A005843, A000384 Sequence in context: A122578 A208648 A005131 * A325772 A226174 A208482 Adjacent sequences:  A105474 A105475 A105476 * A105478 A105479 A105480 KEYWORD nonn,tabl AUTHOR Emeric Deutsch, Apr 09 2005 STATUS approved

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Last modified October 15 12:31 EDT 2019. Contains 328026 sequences. (Running on oeis4.)