104959

Properties

Appears in sequences

• Apéry numbers: a(n) = Sum_{k=0..n} binomial(n,k)^2 * binomial(n+k,k).at n=6A005258
• Crystal ball sequence for A_6 lattice.at n=6A008388
• This table shows the coefficients of combinatorial formulas needed for generating the sequential sums of p-th powers of binomial coefficients C(n,6). The p-th row (p>=1) contains a(i,p) for i=1 to 6*p-5, where a(i,p) satisfies Sum_{i=1..n} C(i+5,6)^p = 7 * C(n+6,7) * Sum_{i=1..6*p-5} a(i,p) * C(n-1,i-1)/(i+6).at n=14A087110
• Prime Apéry B-numbers.at n=2A092828
• a(n) = Sum_{k=1..n} C(n,k)^3 where C(n,k) is binomial(n,k).at n=6A096191
• Number of length-4 0..n arrays with no adjacent pair x,x+1 repeated.at n=17A269657
• Decimal representation of the diagonal from the origin to the corner of the n-th stage of growth of the two-dimensional cellular automaton defined by "Rule 57", based on the 5-celled von Neumann neighborhood.at n=17A285607
• 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=42A290310
• Number of n X 3 0..1 arrays with every element equal to 0, 1, 3, 4, 5 or 7 king-move adjacent elements, with upper left element zero.at n=11A299123
• Primes p such that A001177(p) = (p-1)/7.at n=36A308800
• 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=34A364113
• Primes p such that, if q,r,s are the next three primes, both p*q*r*s - (p+q+r+s) and p*q*r*s + (p+q+r+s) are primes.at n=22A390929
• Prime numbersat n=10021