A371299 E.g.f. satisfies A(x) = 1/(1 + log(1 - 2*x*A(x)^2) / 2).

1, 1, 8, 128, 3128, 103464, 4327376, 219132416, 13037220864, 891482661120, 68898795919872, 5939542370104320, 565085390314014720, 58814874313859198976, 6647869870080852418560, 810941992663677532667904, 106188636284967568536207360, 14856670240947944840012857344

Offset: 0

Author

Seiichi Manyama, Mar 18 2024

Keywords

• nonn

Crossrefs

Cf. A227917, A370938.

Cf. A371297.

Programs

PARI

a(n) = sum(k=0, n, 2^(n-k)*(2*n+k)!*abs(stirling(n, k, 1)))/(2*n+1)!;

Formula

a(n) = (1/(2*n+1)!) * Sum_{k=0..n} 2^(n-k) * (2*n+k)! * |Stirling1(n,k)|.