A370939
Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 + log(1-3*x)/3) ).
Original entry on oeis.org
1, 1, 7, 93, 1848, 49194, 1646352, 66471138, 3145730760, 170825968008, 10472450056632, 715494753359352, 53913145327125840, 4441896708946850880, 397268517350608957440, 38332384702788360859344, 3969252425402471222357760, 439043217473917940361120000
Offset: 0
-
my(N=20, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1+log(1-3*x)/3))/x))
-
a(n) = sum(k=0, n, 3^(n-k)*(n+k)!*abs(stirling(n, k, 1)))/(n+1)!;
A370995
Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 + x^3*log(1-x)) ).
Original entry on oeis.org
1, 0, 0, 0, 24, 60, 240, 1260, 209664, 2056320, 20476800, 221205600, 19370292480, 406935809280, 7376151444480, 131868581644800, 8376837844193280, 282378273124147200, 7891890567682867200, 207283550601631795200, 11520967360247698636800
Offset: 0
-
my(N=30, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1+x^3*log(1-x)))/x))
-
a(n) = sum(k=0, n\4, (n+k)!*abs(stirling(n-3*k, k, 1))/(n-3*k)!)/(n+1);
A377426
E.g.f. satisfies A(x) = 1/(1 + log(1 - x*A(x)^4)).
Original entry on oeis.org
1, 1, 11, 254, 9096, 443874, 27487034, 2065181880, 182545878152, 18562391987880, 2134764133508832, 273978733525211472, 38820518588599921200, 6019219063397716575840, 1013766602891962529642832, 184300120562198063868474624, 35971439241165448281366023424
Offset: 0
-
a(n) = sum(k=0, n, (4*n+k)!*abs(stirling(n, k, 1)))/(4*n+1)!;
A377429
Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 + log(1-x))^4 ).
Original entry on oeis.org
1, 4, 56, 1436, 54540, 2763696, 175688744, 13457185080, 1207241712536, 124205544781728, 14420516981211360, 1865347268407271040, 266056506383725529568, 41485848013549310521536, 7021170794004780911946048, 1281852242007649764308226240, 251124461130948243588667169280
Offset: 0
-
my(N=20, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1+log(1-x))^4)/x))
-
a(n) = 4*sum(k=0, n, (4*n+k+3)!*abs(stirling(n, k, 1)))/(4*n+4)!;
A375899
E.g.f. satisfies A(x) = 1 / (1 + log(1 - x * A(x)^(1/2)))^2.
Original entry on oeis.org
1, 2, 12, 124, 1846, 36128, 879252, 25637680, 872159952, 33933231696, 1486845891696, 72473120203680, 3890486148311040, 228103117063828992, 14504759878784601600, 994346460412330358016, 73107707092779695687040, 5738844073788385570644480
Offset: 0
-
my(N=20, x='x+O('x^N)); Vec(serlaplace((serreverse(x*(1+log(1-x)))/x)^2))
-
a(n) = 2*sum(k=0, n, (n+k+1)!*abs(stirling(n, k, 1)))/(n+2)!;
A375900
E.g.f. satisfies A(x) = 1 / (1 + log(1 - x * A(x)^(1/3)))^3.
Original entry on oeis.org
1, 3, 21, 237, 3738, 76212, 1912350, 57099816, 1979628552, 78224586240, 3472089084072, 171098204829120, 9271248509444544, 548011290335056272, 35095593433694127696, 2421035179995679335360, 178997036386314294247680, 14121215676864610247122560
Offset: 0
-
my(N=20, x='x+O('x^N)); Vec(serlaplace((serreverse(x*(1+log(1-x)))/x)^3))
-
a(n) = 3*sum(k=0, n, (n+k+2)!*abs(stirling(n, k, 1)))/(n+3)!;