A377339 E.g.f. satisfies A(x) = ( 1 + (exp(x*A(x)) - 1)/A(x) )^2.

1, 2, 4, 20, 144, 1332, 15920, 225332, 3758272, 71711540, 1544139216, 37040248500, 979378764320, 28308318200372, 887957701803952, 30043664101434164, 1090686549233837952, 42290355849577306932, 1744321111108101722768, 76261355010301941319604

Offset

0,2

Links

Table of n, a(n) for n=0..19.

Formula

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A377347.

a(n) = 2 * Sum_{k=0..floor((2*n+2)/3)} (2*n-2*k+1)!/(2*n-3*k+2)! * Stirling2(n,k).

Prog

(PARI) a(n) = 2*sum(k=0, (2*n+2)\3, (2*n-2*k+1)!/(2*n-3*k+2)!*stirling(n, k, 2));

Crossrefs

Cf. A377326, A377340.

Cf. A377347.

Sequence in context: A324311 A303671 A330663 * A370766 A102087 A372234

Adjacent sequences: A377336 A377337 A377338 * A377340 A377341 A377342

Keyword

nonn

Author

Seiichi Manyama, Oct 26 2024

Status

approved