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 A056243 Third diagonal of triangle A056242. 2
 1, 9, 41, 146, 456, 1312, 3568, 9312, 23552, 58112, 140544, 334336, 784384, 1818624, 4173824, 9494528, 21430272, 48037888, 107020288, 237109248, 522715136, 1147142144, 2507145216, 5458886656, 11844714496, 25618808832, 55247372288 (list; graph; refs; listen; history; text; internal format)
 OFFSET 3,2 LINKS F. K. Hwang and C. L. Mallows, Enumerating nested and consecutive partitions, J. Combin. Theory Ser. A 70 (1995), no. 2, 323-333. FORMULA a(n) = sum_{0<=j<=n-3} (-1)^(n-3-j)*binomial(n-3, j)*binomial(n+2j-1, 2j), for n>=3. - Pab Ter (pabrlos2(AT)yahoo.com), Nov 06 2005 Conjecture: a(n) = 2^(-6+n)*(32-35*n+9*n^2). G.f.: x^3*(1+3*x-x^2)/(1-2*x)^3. - Colin Barker, Mar 20 2012 MAPLE seq(add((-1)^(n-3-j)*binomial(n-3, j)*binomial(n+2*j-1, 2*j), j=0..n-3), n=3..40); # Pab Ter (pabrlos2(AT)yahoo.com), Nov 06 2005 T:=proc(n, k) local j: if k=1 then 1 elif k<=n then add((-1)^(k-1-j)*binomial(k-1, j)*binomial(n+2*j-1, 2*j), j=0..k-1) else 0 fi end: seq(T(n, n-2), n=3..40); # Pab Ter (pabrlos2(AT)yahoo.com), Nov 06 2005 CROSSREFS Sequence in context: A271663 A034441 A201275 * A083584 A276780 A183916 Adjacent sequences:  A056240 A056241 A056242 * A056244 A056245 A056246 KEYWORD nonn,easy AUTHOR Colin Mallows, Aug 23 2000 EXTENSIONS More terms from Pab Ter (pabrlos2(AT)yahoo.com), Nov 06 2005 STATUS approved

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Last modified June 24 02:27 EDT 2021. Contains 345413 sequences. (Running on oeis4.)