A249794 G.f.: Sum_{n>=0} x^n/(1-x)^(6*n) * Sum_{k=0..n} C(n,k)^2 * x^k.

1, 1, 8, 44, 232, 1253, 6895, 38376, 215396, 1217109, 6914696, 39458777, 226006814, 1298557455, 7481167001, 43200760775, 249977853797, 1449092483085, 8413731049376, 48922225054030, 284830701327470, 1660264158620798, 9687938318036091, 56586034949700662

Offset

0,3

Links

Table of n, a(n) for n=0..23.

Formula

G.f.: (1-x)^5 / sqrt((1 - 3*x + x^2)*(1 - x + 2*x^2 - x^3)*(1 - 8*x + 14*x^2 - 12*x^3 + 5*x^4 - x^5)).

G.f.: (1-x)^5 / sqrt(1 - 12*x + 52*x^2 - 124*x^3 + 206*x^4 - 246*x^5 + 208*x^6 - 120*x^7 + 45*x^8 - 10*x^9 + x^10).

Example

G.f.: A(x) = 1 + x + 8*x^2 + 44*x^3 + 232*x^4 + 1253*x^5 + 6895*x^6 +...
where
A(x) = 1 + x/(1-x)^6*(1+x) + x^2/(1-x)^12*(1+2^2*x+x^2) + x^3/(1-x)^18*(1+3^2*x+3^2*x^2+x^3) + x^4/(1-x)^24*(1+4^2*x+6^2*x^2+4^2*x^3+x^4) + x^5/(1-x)^30*(1+5^2*x+10^2*x^2+10^2*x^3+5^2*x^4+x^5) +...

Prog

(PARI) {a(n)=polcoeff( sum(m=0, n, x^m * sum(k=0, m, binomial(m, k)^2 * x^k) / (1-x +x*O(x^n))^(6*m)), n)}
for(n=0, 30, print1(a(n), ", "))
(PARI) {a(n)=polcoeff( (1-x)^5 / sqrt((1 - 3*x + x^2)*(1 - x + 2*x^2 - x^3)*(1 - 8*x + 14*x^2 - 12*x^3 + 5*x^4 - x^5) +x*O(x^n)), n)}
for(n=0, 30, print1(a(n), ", "))

Crossrefs

Cf. A249946, A249792, A249793.

Sequence in context: A197213 A198768 A082762 * A322498 A147828 A155604

Adjacent sequences: A249791 A249792 A249793 * A249795 A249796 A249797

Keyword

nonn

Author

Paul D. Hanna, Nov 12 2014

Status

approved