Sequences

392,541 sequences

Theta series of laminated lattice LAMBDA_25 with minimal norm 4.A024211
Theta series of laminated lattice LAMBDA_25 with minimal norm 4.
2nd elementary symmetric function of first n+1 positive integers congruent to 1 mod 3.A024212
2nd elementary symmetric function of first n+1 positive integers congruent to 1 mod 3.
a(n) = 3rd elementary symmetric function of first n+2 positive integers congruent to 1 mod 3.A024213
a(n) = 3rd elementary symmetric function of first n+2 positive integers congruent to 1 mod 3.
a(n) = 4th elementary symmetric function of first n+3 positive integers congruent to 1 mod 3.A024214
a(n) = 4th elementary symmetric function of first n+3 positive integers congruent to 1 mod 3.
Sum of squares of first n positive integers congruent to 1 mod 3.A024215
Sum of squares of first n positive integers congruent to 1 mod 3.
a(n) = n-th elementary symmetric function of the first n+1 positive integers congruent to 1 mod 3.A024216
a(n) = n-th elementary symmetric function of the first n+1 positive integers congruent to 1 mod 3.
a(n) = ( Product {k = 1..n} 3*k - 2 ) * ( Sum {k = 1..n} (-1)^(k+1)/(3*k - 2) ).A024217
a(n) = ( Product {k = 1..n} 3*k - 2 ) * ( Sum {k = 1..n} (-1)^(k+1)/(3*k - 2) ).
a(n) = s(1)*s(2)*...*s(n+1)(1/s(2) - 1/s(3) + ... + c/s(n+1)), where c=(-1)^n+1 and s(k) = 3k-2 for k = 1,2,3,...A024218
a(n) = s(1)*s(2)*...*s(n+1)(1/s(2) - 1/s(3) + ... + c/s(n+1)), where c=(-1)^n+1 and s(k) = 3k-2 for k = 1,2,3,...
a(n) = floor( (2nd elementary symmetric function of S(n))/(first elementary symmetric function of S(n)) ), where S(n) = {first n+1 positive integers congruent to 1 mod 3}.A024219
a(n) = floor( (2nd elementary symmetric function of S(n))/(first elementary symmetric function of S(n)) ), where S(n) = {first n+1 positive integers congruent to 1 mod 3}.
a(n) = [ (3rd elementary symmetric function of S(n))/(first elementary symmetric function of S(n)) ], where S(n) = {first n+2 positive integers congruent to 1 mod 3}.A024220
a(n) = [ (3rd elementary symmetric function of S(n))/(first elementary symmetric function of S(n)) ], where S(n) = {first n+2 positive integers congruent to 1 mod 3}.
[ (4th elementary symmetric function of S(n))/(first elementary symmetric function of S(n)) ], where S(n) = {first n+3 positive integers congruent to 1 mod 3}.A024221
[ (4th elementary symmetric function of S(n))/(first elementary symmetric function of S(n)) ], where S(n) = {first n+3 positive integers congruent to 1 mod 3}.
Number of shuffles (perfect faro shuffles with cut) required to return a deck of size n to its original order.A024222
Number of shuffles (perfect faro shuffles with cut) required to return a deck of size n to its original order.
[ (4th elementary symmetric function of S(n))/(2nd elementary symmetric function of S(n)) ], where S(n) = {first n+3 positive integers congruent to 1 mod 3}.A024223
[ (4th elementary symmetric function of S(n))/(2nd elementary symmetric function of S(n)) ], where S(n) = {first n+3 positive integers congruent to 1 mod 3}.
a(n) = floor((4th elementary symmetric function of S(n))/(3rd elementary symmetric function of S(n))), where S(n) = {first n+3 positive integers congruent to 1 mod 3}.A024224
a(n) = floor((4th elementary symmetric function of S(n))/(3rd elementary symmetric function of S(n))), where S(n) = {first n+3 positive integers congruent to 1 mod 3}.
Expansion of tan(sin(x))*x/2.A024225
Expansion of tan(sin(x))*x/2.
Expansion of sin(tan(x))*x/2.A024226
Expansion of sin(tan(x))*x/2.
Expansion of sinh(x)*sin(sin(x))/2.A024227
Expansion of sinh(x)*sin(sin(x))/2.
Expansion of tanh(x)*tan(sin(x))/2.A024228
Expansion of tanh(x)*tan(sin(x))/2.
Expansion of e.g.f.: tanh(x)*sin(tan(x))/2 (even part).A024229
Expansion of e.g.f.: tanh(x)*sin(tan(x))/2 (even part).
Expansion of e.g.f. sin(x)*sin(sinh(x))/2 (even powers only).A024230
Expansion of e.g.f. sin(x)*sin(sinh(x))/2 (even powers only).
Expansion of tanh(tan(x))*sin(x)/2.A024231
Expansion of tanh(tan(x))*sin(x)/2.
Expansion of sinh(sin(x))*sin(x)/2.A024232
Expansion of sinh(sin(x))*sin(x)/2.
Expansion of tan(tanh(x))*sin(x)/2.A024233
Expansion of tan(tanh(x))*sin(x)/2.
Expansion of sin(tan(x)*sin(x))/2.A024234
Expansion of sin(tan(x)*sin(x))/2.
Expansion of e.g.f. tan(x)*sin(x)/2 (even powers only).A024235
Expansion of e.g.f. tan(x)*sin(x)/2 (even powers only).
Expansion of log(1+tan(x)*x)/2.A024236
Expansion of log(1+tan(x)*x)/2.
Expansion of sin(sin(x)*x)/2.A024237
Expansion of sin(sin(x)*x)/2.
Expansion of sinh(sin(x)*x)/2.A024238
Expansion of sinh(sin(x)*x)/2.
Expansion of tanh(tan(x)*sin(x))/2.A024239
Expansion of tanh(tan(x)*sin(x))/2.
Expansion of sinh(tan(x)*sin(x))/2.A024240
Expansion of sinh(tan(x)*sin(x))/2.
E.g.f. tan(x)*sin(tanh(x))/2 (even powers only).A024241
E.g.f. tan(x)*sin(tanh(x))/2 (even powers only).
Expansion of tanh(sin(x))*tan(x)/2.A024242
Expansion of tanh(sin(x))*tan(x)/2.
Expansion of tanh(sin(x)*x)/2.A024243
Expansion of tanh(sin(x)*x)/2.
Expansion of tan(sin(x)*x)/2.A024244
Expansion of tan(sin(x)*x)/2.
Expansion of tan(tan(x)*sin(x))/2.A024245
Expansion of tan(tan(x)*sin(x))/2.
Expansion of tan(sin(x))*sinh(x)/2.A024246
Expansion of tan(sin(x))*sinh(x)/2.
Expansion of e.g.f. sinh(x)*sin(tan(x))/2, even powers only.A024247
Expansion of e.g.f. sinh(x)*sin(tan(x))/2, even powers only.
Expansion of sin(tan(x)*x)/2.A024248
Expansion of sin(tan(x)*x)/2.
Expansion of tanh(tan(x))*tan(x)/2.A024249
Expansion of tanh(tan(x))*tan(x)/2.
Expansion of tan(x)*sin(sinh(x))/2.A024250
Expansion of tan(x)*sin(sinh(x))/2.
Expansion of tan(x)*sinh(sin(x))/2.A024251
Expansion of tan(x)*sinh(sin(x))/2.
Expansion of tan(x)*tan(tanh(x))/2.A024252
Expansion of tan(x)*tan(tanh(x))/2.
Expansion of sin(sin(x))*x/2.A024253
Expansion of sin(sin(x))*x/2.
Expansion of sin(sin(x)^2)/2.A024254
Expansion of sin(sin(x)^2)/2.
a(0)=0, a(n) = n*E(2n-1) for n >= 1, where E(n) = A000111(n) are the Euler (or up-down) numbers.A024255
a(0)=0, a(n) = n*E(2n-1) for n >= 1, where E(n) = A000111(n) are the Euler (or up-down) numbers.
Expansion of log(1+sinh(x)*x)/2.A024256
Expansion of log(1+sinh(x)*x)/2.
Expansion of tanh(tan(x)*x)/2.A024257
Expansion of tanh(tan(x)*x)/2.
Expansion of sinh(sin(x)^2)/2.A024258
Expansion of sinh(sin(x)^2)/2.
Expansion of sinh(tan(x))*sin(x)/2.A024259
Expansion of sinh(tan(x))*sin(x)/2.
Expansion of tan(sinh(x))*sin(x)/2.A024260
Expansion of tan(sinh(x))*sin(x)/2.