A377391 -id:A377391 - cp's OEIS frontend

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

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)! ).

A377686 E.g.f. satisfies A(x) = (1 - x * log(1 - x*A(x)))^3.

Original entry on oeis.org

1, 0, 6, 9, 312, 2070, 53892, 797580, 21541440, 508313232, 15840608400, 502075577520, 18473543511552, 722232734446080, 31135359390952320, 1435933667363963040, 71392285554374384640, 3782802775152784320000, 213512536856209839796224, 12767785967296083820561920

Offset: 0

Seiichi Manyama, Nov 04 2024

nonn

Cf. A371117, A377685.

Cf. A377391, A377687.

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

E.g.f.: B(x)^3, where B(x) is the e.g.f. of A377687.

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

cp's OEIS Frontend

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

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