68712

Appears in sequences

• G.f.: q * Product_{m>=1} (1-q^m)^8*(1-q^2m)^8.at n=23A002288
• Triangle T(n,k) = d(n-k,n), 0 <= k <= n, where d(l,m) = Sum_{k=l..m} 2^k * binomial(2*m-2*k, m-k) * binomial(m+k, m) * binomial(k, l).at n=19A067001
• Coefficients of a polynomial representation of the integral of 1/(x^4 + 2*a*x^2 + 1)^(n+1) from x = 0 to infinity.at n=16A126936
• Averages of twin prime pairs that are sums of 5 consecutive averages of twin prime pairs.at n=18A160919
• Triangle read by rows: T(n,k) is the number of permutations of {1,2,...,n} having k cycles that are either nonincreasing or of length 1 (0<=k<=n). A cycle (b(1), b(2), ...) is said to be increasing if, when written with its smallest element in the first position, it satisfies b(1) < b(2) < b(3) < ... .at n=60A186759
• Expansion of q * (phi(q) * psi(-q))^8 in powers of q where phi(), psi() are Ramanujan theta functions.at n=22A216711
• Number of length n+6 0..4 arrays with no seven consecutive terms having six times any element equal to the sum of the remaining six.at n=0A249315
• T(n,k)=Number of length n+6 0..k arrays with no seven consecutive terms having six times any element equal to the sum of the remaining six.at n=6A249319
• Number of length 1+6 0..n arrays with no seven consecutive terms having six times any element equal to the sum of the remaining six.at n=3A249320
• T(n,k) = Sum_{j=1..n} 2^j*binomial(2*n-2*j, n-j)*binomial(n+j, n)*binomial(j, k), triangle read by rows (n >= 0 and 0 <= k <= n).at n=16A335183