78129765

Appears in sequences

• a(n) = Product_{i=1..n} (2^i - 1). Also called 2-factorial numbers.at n=7A005329
• Array of q-factorial numbers n!_q, read by ascending antidiagonals.at n=47A069777
• A q-factorial type triangle sequence: t(n,m)=Product[Sum[(m + 1)^i, {i, 0, k - 1}], {k, 1, n}].at n=21A156173
• Array A(n, k) = Product_{j=1..n} ( (k+1)^j - 1 ) with A(n, 0) = n!, read by antidiagonals.at n=43A156540
• Square array T(n, k) = Product_{j=1..n} ( Sum_{i=0..j-1} ((k+1)^2 - (k+1))^i ) with T(n, 0) = n!, read by antidiagonals.at n=43A156881
• Triangle T(n, k, q) = t(n,q)/(t(k,q)*t(n-k,q)), where t(n, k) = Product_{j=1..n} q-Pochhammer(j, k+1, k+1)/(1-(k+1))^j and t(n, 0) = n!, with q = 1, read by rows.at n=29A156950
• Triangle T(n, k, q) = t(n,q)/(t(k,q)*t(n-k,q)), where t(n, k) = Product_{j=1..n} q-Pochhammer(j, k+1, k+1)/(1-(k+1))^j and t(n, 0) = n!, with q = 1, read by rows.at n=34A156950
• Triangle T(n, k, q) = c(n, q)/(c(k, q)*c(n-k, q)) where c(n,q) = Product_{j=1..n} (q^j -1)^(n-j) and q = 2, read by rows.at n=37A173503
• Triangle T(n, k, q) = c(n, q)/(c(k, q)*c(n-k, q)) where c(n,q) = Product_{j=1..n} (q^j -1)^(n-j) and q = 2, read by rows.at n=43A173503
• Array: row n shows the coefficients of the characteristic polynomial of the n-th principal submatrix of f(i,j)=(2i-1 if i=j and 1 otherwise) for i>=1 and j>=1 (as in A204131).at n=35A204134
• Triangle of numbers S(n,k) (0 <= k <= n) arising in the enumeration of interval orders without duplicated holdings.at n=28A259876
• Triangle read by rows. T(n,k) is the number of flags in an n dimensional vector space over GF(2) that have length exactly k, n >= 0, 0 <= k <= n.at n=35A289546
• Triangle read by rows: T(n,k) is the number of chains of length k in the partially ordered (by subspace inclusion) set of all subspaces of GF(2)^n, n>=0, 0<=k<=n.at n=35A293845
• G.f. A(x) = Sum_{n>=0} x^n/a(n) satisfies: A(x) = A(x^2) + Integral A(x^2) dx.at n=127A294640
• Square array A(n,k), n >= 0, k >= 1, read by antidiagonals: A(n,k) = Product_{j=1..n} (k^j - 1).at n=43A320354
• Irregular triangle read by rows: T(n, k) is the q-multinomial coefficient defined by the k-th partition of n in Abramowitz-Stegun order, evaluated at q = 2.at n=43A347485