0,2

All upper diagonals of square array A130462 have a g.f. D(x,n) equal to the product of this main diagonal g.f. D(x,0) and a power of G(x), the g.f. of A002293: D(x,n) = D(x,0)*G(x)^n, where G(x) satisfies G(x) = 1 + x*G(x)^4.

Square array A130462 begins:

(1), 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...;

(1), (2), 3, 4, 5, 6, 7, 8, 9, 10, ...;

(3), 7, (12), 18, 25, 33, 42, 52, ...;

(7), 25, 50, (83), 125, 177, 240, ...;

(25), 75, 200, 377, (617), 932, ...;

(75), 275, 652, 1584, 2919, (4759), ...; ...

where row n+1 equals the partial sums of the sequence resulting from removing the terms in the first column and main diagonal from row n.

Cf. A130462 (array), A130463 (first column); A002293.

Sequence in context: A055548 A092850 A052864 this_sequence A006657 A105927 A052887

Adjacent sequences: A130461 A130462 A130463 this_sequence A130465 A130466 A130467

nonn

Paul D. Hanna (pauldhanna(AT)juno.com), May 26 2007