Sequences

392,541 sequences

Index of central binomial coefficient C(2n,n) within A006987.A009561
Index of central binomial coefficient C(2n,n) within A006987.
Expansion of e.g.f. sin(x/cos(x)) (odd powers only).A009562
Expansion of e.g.f. sin(x/cos(x)) (odd powers only).
Expansion of e.g.f. sin(x/cosh(x)) (odd powers only).A009563
Expansion of e.g.f. sin(x/cosh(x)) (odd powers only).
E.g.f. sin(x^2)/2, coefficients of x^(4*n + 2).A009564
E.g.f. sin(x^2)/2, coefficients of x^(4*n + 2).
Expansion of e.g.f. sinh(exp(x)*x).A009565
Expansion of e.g.f. sinh(exp(x)*x).
Expansion of e.g.f. sinh(log(1+log(1+x))).A009566
Expansion of e.g.f. sinh(log(1+log(1+x))).
Expansion of e.g.f.: sinh(log(1 + sin(x))).A009567
Expansion of e.g.f.: sinh(log(1 + sin(x))).
Expansion of e.g.f.: sinh(log(1+sinh(x))).A009568
Expansion of e.g.f.: sinh(log(1+sinh(x))).
Expansion of e.g.f. sinh(log(1+tan(x))).A009569
Expansion of e.g.f. sinh(log(1+tan(x))).
Expansion of e.g.f. sinh(log(1+tanh(x))).A009570
Expansion of e.g.f. sinh(log(1+tanh(x))).
Least m such that if a/b < c/d are Farey fractions of order n then there exists k such that a/b < k/m < c/d, k/m reduced.A009571
Least m such that if a/b < c/d are Farey fractions of order n then there exists k such that a/b < k/m < c/d, k/m reduced.
Expansion of e.g.f. sinh(log(1+x))*cos(x).A009572
Expansion of e.g.f. sinh(log(1+x))*cos(x).
Expansion of e.g.f. sinh(log(1+x))*cosh(x).A009573
Expansion of e.g.f. sinh(log(1+x))*cosh(x).
Expansion of e.g.f. sinh(log(1+x))*exp(x).A009574
Expansion of e.g.f. sinh(log(1+x))*exp(x).
E.g.f. sinh(log(1+x))*log(1+x).A009575
E.g.f. sinh(log(1+x))*log(1+x).
Expansion of e.g.f. sinh(log(1+x))/cos(x).A009576
Expansion of e.g.f. sinh(log(1+x))/cos(x).
Expansion of e.g.f. sinh(log(1+x))/cosh(x).A009577
Expansion of e.g.f. sinh(log(1+x))/cosh(x).
E.g.f. sinh(log(1+x))/exp(x). Unsigned sequence gives degrees of (finite by nilpotent) representations of Braid groups.A009578
E.g.f. sinh(log(1+x))/exp(x). Unsigned sequence gives degrees of (finite by nilpotent) representations of Braid groups.
Expansion of e.g.f. sinh(log(1+x)*cos(x)).A009579
Expansion of e.g.f. sinh(log(1+x)*cos(x)).
Expansion of e.g.f. sinh(log(1+x)*cosh(x)).A009580
Expansion of e.g.f. sinh(log(1+x)*cosh(x)).
Expansion of e.g.f. sinh(log(1+x)*exp(x)).A009581
Expansion of e.g.f. sinh(log(1+x)*exp(x)).
Expansion of e.g.f.: sinh(log(1+x)/cos(x)).A009582
Expansion of e.g.f.: sinh(log(1+x)/cos(x)).
Expansion of e.g.f. sinh(log(1+x)/cosh(x)).A009583
Expansion of e.g.f. sinh(log(1+x)/cosh(x)).
Expansion of e.g.f. sinh(log(1+x)/exp(x)).A009584
Expansion of e.g.f. sinh(log(1+x)/exp(x)).
E.g.f. sinh(log(1+x)^2).A009585
E.g.f. sinh(log(1+x)^2).
Expansion of e.g.f. sinh(sin(log(1+x))).A009586
Expansion of e.g.f. sinh(sin(log(1+x))).
Expansion of e.g.f. sinh(sin(sin(x))).A009587
Expansion of e.g.f. sinh(sin(sin(x))).
Expansion of e.g.f. sinh(sin(tan(x))), odd powers only.A009588
Expansion of e.g.f. sinh(sin(tan(x))), odd powers only.
If i < n, j < n, p/a(i) < q/a(j), then there exists k with p/a(i) < k/a(n) < q/a(j).A009589
If i < n, j < n, p/a(i) < q/a(j), then there exists k with p/a(i) < k/a(n) < q/a(j).
Expansion of e.g.f. sinh(sin(x))*exp(x).A009590
Expansion of e.g.f. sinh(sin(x))*exp(x).
Expansion of e.g.f. sinh(sin(x)) * sin(x) (even powers only).A009591
Expansion of e.g.f. sinh(sin(x)) * sin(x) (even powers only).
Expansion of e.g.f. sinh(sin(x))/cos(x) (odd powers only).A009592
Expansion of e.g.f. sinh(sin(x))/cos(x) (odd powers only).
Expansion of e.g.f. sinh(sin(x)*cos(x)), odd powers only.A009593
Expansion of e.g.f. sinh(sin(x)*cos(x)), odd powers only.
Expansion of e.g.f. sinh(sin(x)*exp(x)).A009594
Expansion of e.g.f. sinh(sin(x)*exp(x)).
Expansion of e.g.f. sinh(sin(x)*x), even powers only.A009595
Expansion of e.g.f. sinh(sin(x)*x), even powers only.
Expansion of e.g.f. sinh(sin(x)^2) (even powers only).A009596
Expansion of e.g.f. sinh(sin(x)^2) (even powers only).
Expansion of sinh(sinh(log(1+x))).A009597
Expansion of sinh(sinh(log(1+x))).
Expansion of e.g.f. sinh(sinh(x))*exp(x).A009598
Expansion of e.g.f. sinh(sinh(x))*exp(x).
Expansion of e.g.f. sinh(sinh(x)*exp(x)).A009599
Expansion of e.g.f. sinh(sinh(x)*exp(x)).
Expansion of e.g.f. sin(tan(x))*x/2 (even powers only).A009600
Expansion of e.g.f. sin(tan(x))*x/2 (even powers only).
Expansion of e.g.f.: sinh(tan(log(1+x))).A009601
Expansion of e.g.f.: sinh(tan(log(1+x))).
Expansion of e.g.f. sinh(tan(sin(x))) (odd powers only).A009602
Expansion of e.g.f. sinh(tan(sin(x))) (odd powers only).
Expansion of sinh(tan(tan(x))) (odd powers only).A009603
Expansion of sinh(tan(tan(x))) (odd powers only).
Expansion of e.g.f. sinh(tan(x))*cos(x), odd powers only.A009604
Expansion of e.g.f. sinh(tan(x))*cos(x), odd powers only.
Expansion of e.g.f. sinh(tan(x))*exp(x).A009605
Expansion of e.g.f. sinh(tan(x))*exp(x).
Expansion of e.g.f. sinh(tan(x))*sin(x) (even powers only).A009606
Expansion of e.g.f. sinh(tan(x))*sin(x) (even powers only).
Expansion of e.g.f. sinh(tan(x))/cos(x), odd powers only.A009607
Expansion of e.g.f. sinh(tan(x))/cos(x), odd powers only.
Expansion of e.g.f. sinh(tan(x)*exp(x)).A009608
Expansion of e.g.f. sinh(tan(x)*exp(x)).
sinh(tan(x)*sin(x))=2/2!*x^2+4/4!*x^4+182/6!*x^6+4744/8!*x^8...A009609
sinh(tan(x)*sin(x))=2/2!*x^2+4/4!*x^4+182/6!*x^6+4744/8!*x^8...
sinh(sinh(x)*tan(x)) = 2/2!*x^2 + 12/4!*x^4 + 262/6!*x^6 + 13272/8!*x^8 + ...A009610
sinh(sinh(x)*tan(x)) = 2/2!*x^2 + 12/4!*x^4 + 262/6!*x^6 + 13272/8!*x^8 + ...