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

Author

Colin Mallows, Aug 23 2000

Keywords

• nonn
• easy

Links

• F. K. Hwang and C. L. Mallows, Enumerating nested and consecutive partitions, J. Combin. Theory Ser. A 70 (1995), no. 2, 323-333.

Crossrefs

Cf. A056242.

Programs

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

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

Extensions

More terms from Pab Ter (pabrlos2(AT)yahoo.com), Nov 06 2005