A056243 Third diagonal of triangle A056242.

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

Offset

3,2

Links

Table of n, a(n) for n=3..29.

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

Cf. A056242.

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