A377347 -id:A377347 - cp's OEIS frontend

A377348 E.g.f. satisfies A(x) = 1 + (exp(x*A(x)^3) - 1)/A(x)^3.

1, 1, 1, 10, 79, 946, 14653, 267478, 5817187, 145061146, 4089128425, 128703410254, 4470302200087, 169912192575490, 7014628977829237, 312570024564324358, 14952747796689292747, 764341021646724256426, 41578052013117358139809, 2398149800670737138081470

Offset: 0

Seiichi Manyama, Oct 26 2024

nonn

Cf. A052752, A367135, A367181, A377324, A377328.

Cf. A377326, A377347.

a(n) = sum(k=0, (3*n+1)\4, (3*n-3*k)!/(3*n-4*k+1)!*stirling(n, k, 2));

a(n) = Sum_{k=0..floor((3*n+1)/4)} (3*n-3*k)!/(3*n-4*k+1)! * Stirling2(n,k).

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

Original entry on oeis.org

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

Offset: 0

Seiichi Manyama, Oct 26 2024

nonn

Cf. A377326, A377340.

Cf. A377347.

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

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).

cp's OEIS Frontend

A377348 E.g.f. satisfies A(x) = 1 + (exp(x*A(x)^3) - 1)/A(x)^3.

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