A377360 -id:A377360 - cp's OEIS frontend

A377361 E.g.f. satisfies A(x) = ( 1 - log(1 - x*A(x)) )^3.

1, 3, 27, 435, 10308, 324942, 12831540, 610024398, 33948639024, 2165995595208, 155913776865216, 12501945620113320, 1105228405532295216, 106806396107364409440, 11201958792185117156640, 1267313834232739887340464, 153842580381390055963315200, 19946923686925035463312117632

Offset: 0

Seiichi Manyama, Oct 26 2024

nonn

Index entries for reversions of series

Cf. A138013, A377360.

Cf. A136719, A367152, A376393.

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

E.g.f.: B(x)^3, where B(x) is the e.g.f. of A367152.
a(n) = 3 * (3*n+2)! * Sum_{k=0..n} |Stirling1(n,k)|/(3*n-k+3)!.
E.g.f.: (1/x) * Series_Reversion( x/(1 - log(1-x))^3 ).

A377390 Expansion of e.g.f. (1/x) * Series_Reversion( x/(1 - x*log(1-x))^2 ).

Original entry on oeis.org

1, 0, 4, 6, 232, 1380, 46308, 593880, 20639456, 434113344, 16557009840, 490894572960, 20995513516800, 801146038080960, 38632110899469696, 1791609186067646400, 97167945389675212800, 5275541489312858803200, 319879838094553691744256, 19820894989178283188198400

Offset: 0

Seiichi Manyama, Oct 27 2024

nonn

Index entries for reversions of series

Cf. A371121, A377391.

Cf. A371229, A377360.

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

E.g.f. A(x) satisfies A(x) = ( 1 - x*A(x)*log(1 - x*A(x)) )^2.
E.g.f.: B(x)^2, where B(x) is the e.g.f. of A371229.
a(n) = 2 * n! * (2*n+1)! * Sum_{k=0..floor(n/2)} |Stirling1(n-k,k)|/( (n-k)! * (2*n-k+2)! ).

cp's OEIS Frontend

A377361 E.g.f. satisfies A(x) = ( 1 - log(1 - x*A(x)) )^3.

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