A386264 G.f. A(x) satisfies A(x) = 1/( (1-x)^3 * (1 - x*A(x) - 2*x^2*A'(x)) ).

1, 4, 22, 190, 2239, 32431, 546832, 10414132, 219845677, 5079617326, 127292440606, 3435881715553, 99351006910147, 3063829146597493, 100385767850729656, 3483114440490487576, 127610457725933245753, 4923678697863463464970, 199592119100636938629838

Offset

0,2

Links

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

Formula

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

a(n) = binomial(n+2,2) + 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)^3 * (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]=binomial(i+2, 2)+i*sum(j=0, i-1, v[j+1]*v[i-j])); v;

Crossrefs

Cf. A376125, A386263.

Cf. A386210, A386230.

Sequence in context: A112370 A197961 A203120 * A002728 A364624 A062494

Adjacent sequences: A386261 A386262 A386263 * A386265 A386266 A386267

Keyword

nonn

Author

Seiichi Manyama, Jul 17 2025

Status

approved