A086611 Row sums of triangle of coefficients (A086610) where T(n,k) is the coefficient of x^n*y^k in f(x,y) that satisfies f(x,y) = (1-x-x^2)/(1-x)^2 + xy*f(x,y)^2.

1, 2, 4, 11, 36, 129, 486, 1892, 7546, 30675, 126642, 529600, 2238782, 9551583, 41075698, 177865921, 774875488, 3393896499, 14936139018, 66014016044, 292892796930, 1304062558529, 5824639004518, 26091657768331, 117190470415840, 527653882992389, 2381172879946750, 10768255221189926

Offset

0,2

Links

Table of n, a(n) for n=0..27.

Formula

G.f.: A(x) = (1-x-x^2)/(1-x)^2 + x*A(x)^2.

From Seiichi Manyama, Mar 03 2026: (Start)

a(0) = 1; a(n) = 2 - n + Sum_{k=0..n-1} a(k) * a(n-1-k).

G.f.: (1 - sqrt(1 - 4*x*(1 + 2*x/(1-x) - x/(1-x)^2)))/(2*x). (End)

Example

a(3) = -1+1+6+5 = 11, a(4) = -2-2+6+20+14 = 36, a(5) = -3-6-4+30+70+42 = 129.

Crossrefs

Cf. A086610 (triangle), A086616, A086632, A110886.

Sequence in context: A193058 A179379 A387692 * A035098 A328425 A174107

Adjacent sequences: A086608 A086609 A086610 * A086612 A086613 A086614

Keyword

nonn,easy

Author

Paul D. Hanna, Jul 24 2003

Status

approved