A381173
Expansion of e.g.f. (1/x) * Series_Reversion( x / (1 + x*cos(x)) ).
Original entry on oeis.org
1, 1, 2, 3, -24, -475, -5760, -52297, -155008, 8781705, 313344000, 6966991339, 102864807936, 18664712365, -71473582229504, -3387816787568865, -103478592573112320, -1899945146589964783, 18941335827815596032, 3808766537454425974739, 215681241589289359769600
Offset: 0
-
a185951(n, k) = binomial(n, k)/2^k*sum(j=0, k, (2*j-k)^(n-k)*binomial(k, j));
a(n) = sum(k=0, n, k!*binomial(n+1, k)*I^(n-k)*a185951(n, k))/(n+1);
A381174
Expansion of e.g.f. (1/x) * Series_Reversion( x * (1 - x*cos(x)) ).
Original entry on oeis.org
1, 1, 4, 27, 264, 3365, 52800, 980903, 20984320, 506078505, 13525493760, 394758794419, 12414039171072, 414990179398093, 14523823020621824, 521523225315049215, 18594912994237808640, 613842569215361446097, 14735570097970682265600, -228398321523777856462261
Offset: 0
-
a185951(n, k) = binomial(n, k)/2^k*sum(j=0, k, (2*j-k)^(n-k)*binomial(k, j));
a(n) = sum(k=0, n, k!*binomial(n+k+1, k)/(n+k+1)*I^(n-k)*a185951(n, k));
A381176
E.g.f. A(x) satisfies A(x) = 1 + x*cos(x*A(x)).
Original entry on oeis.org
1, 1, 0, -3, -24, -55, 480, 8813, 61824, -264591, -13662720, -185252771, -117427200, 52162650553, 1214778679296, 7998339208845, -370278535495680, -14623177924271263, -202753399336206336, 3863010744775239101, 286065782789626920960, 6603193175290504771881
Offset: 0
-
a185951(n, k) = binomial(n, k)/2^k*sum(j=0, k, (2*j-k)^(n-k)*binomial(k, j));
a(n) = sum(k=0, n, k!*binomial(n-k+1, k)/(n-k+1)*I^(n-k)*a185951(n, k));
A381172
E.g.f. A(x) satisfies A(x) = 1/( 1 - x * A(x)^2 * cosh(x * A(x)) ).
Original entry on oeis.org
1, 1, 6, 75, 1416, 36065, 1160400, 45182347, 2066343552, 108594342369, 6449557524480, 427226389872491, 31230489190382592, 2497416890105693569, 216875134620623990784, 20324880119519860657515, 2044641793664946681446400, 219762483007148574205773377, 25134006030221243013604835328
Offset: 0
-
a185951(n, k) = binomial(n, k)/2^k*sum(j=0, k, (2*j-k)^(n-k)*binomial(k, j));
a(n) = sum(k=0, n, k!*binomial(n+2*k+1, k)/(n+2*k+1)*a185951(n, k));
Showing 1-4 of 4 results.
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