A073156 Main diagonal sequence of triangle A073153.

1, 2, 9, 36, 156, 698, 3210, 15080, 72060, 349184, 1711869, 8475494, 42318018, 212843826, 1077391794, 5484472880, 28058940086, 144195777552, 744017466318, 3852968380624, 20019113126120, 104329129258596, 545214946753377

Offset: 0

Author

Paul D. Hanna, Jul 29 2002

Keywords

• easy
• nonn

Crossrefs

Cf. A073153, A073155, A073157.

Programs

PARI

a(n, r=2, s=2, t=2, u=0) = r*sum(k=0, n, binomial(t*k+u*(n-k)+r, k)*binomial(s*k, n-k)/(t*k+u*(n-k)+r)); \\ Seiichi Manyama, Dec 07 2024

Formula

Convolution of sequence A073155: a(n) = Sum_{k=0..n} A073155(k) * A073155(n-k).

G.f.: 1/4*(1-(1-4*x*(1+x)^2)^(1/2))^2/x^2/(1+x)^4. - Vladeta Jovovic, Oct 10 2003

From Seiichi Manyama, Dec 07 2024: (Start)

G.f. A(x) satisfies A(x) = ( 1 + x * (1 + x)^2 * A(x) )^2.

a(n) = Sum_{k=0..n} binomial(2*k+2,k) * binomial(2*k,n-k)/(k+1). (End)

Extensions

More terms from Vladeta Jovovic, Oct 10 2003