108056025

Appears in sequences

• Number of permutations in the symmetric group S_n that have odd order.at n=12A000246
• Squares of double factorials: (1*3*5*...*(2n-1))^2 = ((2*n-1)!!)^2.at n=6A001818
• Triangle of central factorial numbers |4^k t(2n+1,2n+1-2k)| read by rows (n>=0, k=0..n).at n=27A008956
• Expansion of e.g.f. exp(arcsinh(arcsin(x))).at n=13A012248
• exp(arcsinh(arcsinh(x))) = 1+x+1/2!*x^2-1/3!*x^3-7/4!*x^4+9/5!*x^5...at n=13A012252
• Triangle T(n,k) defined by the generating function cosh(sqrt(y)*arcsin(x)) + sqrt(y)*sinh(sqrt(y)*arcsin(x)) - 1 = Sum_{n>=1} Sum_{k=1..n} T(n,k)*y^k *x^n/n!.at n=42A091885
• Row 2 of array in A288580.at n=11A092396
• Exponential (binomial) convolution of A001818 (with interspersed zeros) and A000142 (factorials).at n=10A111601
• Table of the number of (n,k)-Riordan complexes, read by rows.at n=21A160563
• Expansion of e.g.f. arcsin(x).at n=12A177145
• Triangle read by rows: coefficients in expansion of Q(n) = (x-n^2)*(x-(n-2)^2)*(x-(n-4)^2)*...*(x-(1 or 2)^2), highest powers first.at n=47A182971
• a(n) = n^2*(n-2)^2*(n-4)^2*...*(1 or 2)^2.at n=11A184877
• E.g.f. log(1 + sin(arctan(x))).at n=13A191011
• 1^2 * 3^2 * 5^2 * ... * (p-4)^2 * (p-2)^2 where p is the n-th prime number (n >= 2).at n=4A218536
• Triangular array read by rows. Row n lists the coefficients of the closed form of hypergeometric([1/2, -n/2, (1-n)/2], [], 4*z).at n=42A246256
• Number of permutations on [n] admitting an eighth root.at n=12A247006
• Triangle read by rows, T(n,k) = Sum_{j=k..n} A269940(n,j)*A269939(j,k), for n>=0 and 0<=k<=n.at n=27A269957
• Numerators of bivariate Taylor expansion of the incomplete elliptic integral of the first kind.at n=27A272102
• E.g.f. A(x,k) satisfies: sn(A(x,k), k) = k * sn(x,k), where sn(,) and cn(,) are Jacobi Elliptic functions.at n=48A291527
• E.g.f. A(x,k) satisfies: sin(A(x,k)) = k * sin(x).at n=27A291560