A281548 Number of distinct monomials in the expansion of Product_{i=1..n} (y_1+...+y_i+x_i+x_{i+1}).

1, 3, 11, 46, 210, 1018, 5150, 26889, 143829, 784167, 4341843, 24348352, 138007784, 789375504, 4550522248

Offset

0,2

Links

Table of n, a(n) for n=0..14.

T. Amdeberhan, M. Alekseyev, Expanding into monomials, MathOverflow, 2017.

Prog

(SageMath)
def A281548(n):
  R.<x> = PowerSeriesRing(ZZ)
  return sum(sum(
      ( prod(1 + (1-2*x+O(x^(k+1)))^(-c[i]-1)
        for i in range(n-k) )
      ) * (1-2*x+O(x^(k+1)))^(-(n-k-sum(c))-1) / 2^(n-k)
    for c in map(lambda t: t.to_Catalan_code(), DyckWords(n-k)) )[k]
  for k in range(n+1) )

Crossrefs

Cf. A000108, A006318.

Sequence in context: A287891 A371428 A233389 * A086521 A225293 A046996

Adjacent sequences: A281545 A281546 A281547 * A281549 A281550 A281551

Keyword

nonn,more

Author

Max Alekseyev, Jan 23 2017

Status

approved