A370941
Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 + 2*log(1-x)) ).
Original entry on oeis.org
1, 2, 18, 304, 7668, 259048, 11001968, 563728464, 33857839360, 2333472749376, 181558569560448, 15743501573763456, 1505641080366272640, 157445985444107880960, 17872580693502293022720, 2188829492626563123881472, 287673783237906407512565760
Offset: 0
-
my(N=20, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1+2*log(1-x)))/x))
-
a(n) = sum(k=0, n, 2^k*(n+k)!*abs(stirling(n, k, 1)))/(n+1)!;
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)!;
A377737
Expansion of e.g.f. (1/x) * Series_Reversion( x/(1 - log(1-2*x) / 2) ).
Original entry on oeis.org
1, 1, 4, 32, 392, 6504, 136464, 3466224, 103425664, 3546396288, 137423600640, 5939224680960, 283254408582144, 14777481937449984, 837175325044101120, 51182161648716349440, 3358765321328869539840, 235492308312669671424000, 17568539556367396687183872
Offset: 0
-
my(N=20, x='x+O('x^N)); Vec(serlaplace(serreverse(x/(1-log(1-2*x)/2))/x))
-
a(n) = n!*sum(k=0, n, 2^(n-k)*abs(stirling(n, k, 1))/(n-k+1)!);
A371299
E.g.f. satisfies A(x) = 1/(1 + log(1 - 2*x*A(x)^2) / 2).
Original entry on oeis.org
1, 1, 8, 128, 3128, 103464, 4327376, 219132416, 13037220864, 891482661120, 68898795919872, 5939542370104320, 565085390314014720, 58814874313859198976, 6647869870080852418560, 810941992663677532667904, 106188636284967568536207360, 14856670240947944840012857344
Offset: 0
-
a(n) = sum(k=0, n, 2^(n-k)*(2*n+k)!*abs(stirling(n, k, 1)))/(2*n+1)!;
Showing 1-4 of 4 results.