A160568 Diagonal sums of number triangle [k<=n]*C(n,2n-2k)3^(n-k)A000108(n-k).

1, 0, 1, 3, 1, 9, 19, 18, 91, 165, 271, 990, 1765, 3843, 11467, 21630, 53299, 140724, 287119, 736101, 1818235, 3982044, 10225117, 24521409, 56584243, 143641017, 341948179, 816095982, 2045559205, 4888806237, 11897144767, 29540684052

Offset: 0

Author

Paul Barry, May 19 2009

Keywords

• easy
• nonn

Comments

Hankel transform is A160569(n+1).

Crossrefs

Cf.: A025250, A160565.

Formula

G.f.: (1-x^2-sqrt(1-2x^2-12x^3+x^4))/(6*x^3);

G.f.: 1/(1-x^2-3*x^3/(1-x^2-3*x^3/(1-x^2-3*x^3/(1-x^2-3*x^3/(1-... (continued fraction).

a(n)=sum{k=0..floor(n/2), C(n-k,2n-4k)*3^(n-2k)*A000108(n-2k)};

a(n)=sum{k=0..n, C(n-k/2,2(n-k))*3^(n-k)*A000108(n-k)*(1+(-1)^k)/2};

a(n)=sum{k=0..n, C((n+k)/2,2k)*3^k*A000108(k)(1+(-1)^(n-k))/2}.