1004307

Appears in sequences

• Apéry numbers: a(n) = Sum_{k=0..n} binomial(n,k)^2 * binomial(n+k,k).at n=7A005258
• Crystal ball sequence for A_7 lattice.at n=7A008390
• This table shows the coefficients of combinatorial formulas needed for generating the sequential sums of p-th powers of binomial coefficients C(n,7). The p-th row (p>=1) contains a(i,p) for i=1 to 7*p-6, where a(i,p) satisfies Sum_{i=1..n} C(i+6,7)^p = 8 * C(n+7,8) * Sum_{i=1..7*p-6} a(i,p) * C(n-1,i-1)/(i+7).at n=16A087111
• Irregular triangle read by rows. Row n gives the coefficients of the polynomial multiplying the exponential function in the e.g.f. of the (n+1)-th diagonal sequences of triangle A008459 (Pascal squares). T(n,k) for n >= 0 and k = 0..2*n.at n=56A290310
• Square array read by ascending antidiagonals: T(n,k) = [x^k] 1/(1 - x) * Legendre_P(k, (1 + x)/(1 - x))^n for n, k >= 0.at n=43A364113