55152

Appears in sequences

• E.g.f. sinh(log(1+x))*log(1+x).at n=8A009575
• Convolution of Catalan numbers A000108(n+1), n >= 0, with A020918.at n=5A041005
• Triangle read by rows. Let q(x,n) = -((x - 1)^(2*n + 1)/x^n)*Sum[(k + n)^n*Binomial[k, n]*x^k, {k, 0, Infinity}]; p(x,n)=q(x,n)+x^n*q(1/x,n); then row n gives coefficients of p(x,n).at n=16A155951
• Triangle read by rows. Let q(x,n) = -((x - 1)^(2*n + 1)/x^n)*Sum[(k + n)^n*Binomial[k, n]*x^k, {k, 0, Infinity}]; p(x,n)=q(x,n)+x^n*q(1/x,n); then row n gives coefficients of p(x,n).at n=17A155951
• Triangle related to the divergent series 1^m*1! - 2^m*2! + 3^m*3! - 4^m*4! + ... for m >= -1.at n=62A163940
• Fourth right hand column of triangle A163940.at n=7A163941
• Numbers k such that the decimal digits of k*(k+1) are a permutation of those of k*(k-1).at n=21A181775
• The number of cycles over all even permutations of {1,2,...,n}.at n=8A226170
• Irregular triangle read by rows: T(n,k) (n>=2, 1<=k<=n) gives number of arrangements of the elements from the multiset M(n, 2) into exactly k disjoint cycles.at n=36A245182
• Triangle read by rows: T(n,m) (n >= 1, 1 <= m <= n) = number of set partitions of [n], avoiding 12343, with m blocks.at n=58A250118
• Number A(n,k) of permutations p of [n] such that the up-down signature of p has nonnegative partial sums with a maximal value <= k; square array A(n,k), n>=0, k>=0, read by antidiagonals.at n=75A262124
• Number of permutations p of [n] such that the up-down signature of p has nonnegative partial sums with a maximal value <= 2.at n=9A262126