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

0,2

Links

Table of n, a(n) for n=0..22.

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)

Prog

(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

Crossrefs

Cf. A073153, A073155, A073157.

Sequence in context: A121769 A006782 A150968 * A150969 A150970 A150971

Adjacent sequences: A073153 A073154 A073155 * A073157 A073158 A073159

Keyword

easy,nonn

Author

Paul D. Hanna, Jul 29 2002

Extensions

More terms from Vladeta Jovovic, Oct 10 2003

Status

approved