A182152 G.f.: [Sum_{n>=0} x^(n*(n+1)/2) * (1+x)^n ]^3.

1, 3, 6, 10, 18, 27, 37, 54, 81, 106, 132, 180, 245, 306, 381, 493, 612, 729, 910, 1173, 1434, 1662, 1950, 2379, 2925, 3522, 4146, 4831, 5628, 6600, 7852, 9363, 10836, 12169, 13947, 16734, 20040, 22875, 25185, 28003, 32403, 38622, 45658, 51810, 56643, 62263, 71310

Offset

0,2

Comments

Equals the self-convolution cube of the flattened Pascal's triangle (A007318).

Links

Paul D. Hanna, Table of n, a(n) for n = 0..1035

Formula

G.f.: [Sum_{n>=0} (1+x)^n*x^n * Product_{k=1..n} (1 - (1+x)*x^(2*k-1)) / (1 - (1+x)*x^(2*k)) ]^3.

Example

G.f.: A(x) = 1 + 3*x + 6*x^2 + 10*x^3 + 18*x^4 + 27*x^5 + 37*x^6 + 54*x^7 + 81*x^8 + 106*x^9 + 132*x^10 +...
such that
A(x)^(1/3) = 1 + x*(1+x) + x^3*(1+x)^2 + x^6*(1+x)^3 + x^10*(1+x)^4 +...

Prog

(PARI) {a(n)=local(A=sum(m=0, (sqrt(8*n+1)+1)\2, x^(m*(m+1)/2)*(1+x+x*O(x^n))^m)); polcoeff(A^3, n)}
for(n=0, 66, print1(a(n), ", "))

Crossrefs

Cf. A152037, A007318.

Sequence in context: A242525 A266617 A291608 * A170803 A182908 A076251

Adjacent sequences: A182149 A182150 A182151 * A182153 A182154 A182155

Keyword

nonn

Author

Paul D. Hanna, Apr 18 2012

Status

approved