A386263 G.f. A(x) satisfies A(x) = 1/( (1-x)^2 * (1 - x*A(x) - 2*x^2*A'(x)) ).

1, 3, 15, 121, 1333, 18091, 286867, 5158385, 103226313, 2269474723, 54307112951, 1404350909545, 39020894189245, 1159475912653163, 36695329075865083, 1232560854783934561, 43801551907551784721, 1642199848241650875907, 64789265823476378293855

Offset

0,2

Links

Table of n, a(n) for n=0..18.

Formula

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

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

Mathematica

terms=19; A[_]=1; Do[A[x_]=1/( (1-x)^2 * (1 - x*A[x] - 2*x^2*A'[x]) ) + O[x]^terms // Normal, terms]; CoefficientList[A[x], x] (* Stefano Spezia, Jul 17 2025 *)

Prog

(PARI) a_vector(n) = my(v=vector(n+1)); for(i=0, n, v[i+1]=i+1+i*sum(j=0, i-1, v[j+1]*v[i-j])); v;

Crossrefs

Cf. A376125, A386264.

Cf. A386209, A386229.

Sequence in context: A156360 A377105 A160884 * A173468 A380774 A197505

Adjacent sequences: A386260 A386261 A386262 * A386264 A386265 A386266

Keyword

nonn

Author

Seiichi Manyama, Jul 17 2025

Status

approved