A377350 -id:A377350 - cp's OEIS frontend

A377349 E.g.f. satisfies A(x) = 1 - log(1 - x*A(x)^2)/A(x)^2.

1, 1, 1, 8, 62, 744, 11102, 201704, 4323720, 106591584, 2974873656, 92674125840, 3188299718496, 120053825169888, 4911082489042992, 216879763758962688, 10283600782413709056, 521088305671611058176, 28101278301136842204288, 1606968565080853531472640

Offset: 0

Seiichi Manyama, Oct 26 2024

nonn

Cf. A365438, A367080, A367138, A377329.

Cf. A377325, A377350.

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

a(n) = Sum_{k=0..floor((2*n+1)/3)} (2*n-2*k)!/(2*n-3*k+1)! * |Stirling1(n,k)|.

A377359 E.g.f. satisfies A(x) = ( 1 - log(1 - x*A(x))/A(x) )^3.

Original entry on oeis.org

1, 3, 9, 57, 642, 9402, 177198, 4051338, 108926520, 3371293704, 118000461528, 4609447152120, 198791258476176, 9381618706074768, 480921576177145392, 26610634173004959312, 1580792845661466884352, 100345182367660427554560, 6778517964127816222982016

Offset: 0

Seiichi Manyama, Oct 26 2024

nonn

Cf. A377325, A377358.

Cf. A377350.

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

E.g.f.: B(x)^3, where B(x) is the e.g.f. of A377350.

a(n) = 3 * Sum_{k=0..floor((3*n+3)/4)} (3*n-3*k+2)!/(3*n-4*k+3)! * |Stirling1(n,k)|.

cp's OEIS Frontend

A377349 E.g.f. satisfies A(x) = 1 - log(1 - x*A(x)^2)/A(x)^2.

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