A249793 G.f.: Sum_{n>=0} x^n/(1-x)^(5*n) * Sum_{k=0..n} C(n,k)^2 * x^k.

1, 1, 7, 35, 171, 856, 4359, 22446, 116557, 609289, 3202088, 16902558, 89550391, 475922764, 2536113322, 13545996260, 72500109601, 388730700761, 2087639484747, 11227578293407, 60461487361452, 325972272495485, 1759323533735344, 9504604121313715, 51393787321667969, 278127959744155754

Offset

0,3

Links

Table of n, a(n) for n=0..25.

Formula

G.f.: (1-x)^4 / sqrt(1 - 10*x + 33*x^2 - 56*x^3 + 66*x^4 - 54*x^5 + 28*x^6 - 8*x^7 + x^8).

Example

G.f.: A(x) = 1 + x + 7*x^2 + 35*x^3 + 171*x^4 + 856*x^5 + 4359*x^6 +...
where
A(x) = 1 + x/(1-x)^5*(1+x) + x^2/(1-x)^10*(1+2^2*x+x^2) + x^3/(1-x)^15*(1+3^2*x+3^2*x^2+x^3) + x^4/(1-x)^20*(1+4^2*x+6^2*x^2+4^2*x^3+x^4) + x^5/(1-x)^25*(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))^(5*m)), n)}
for(n=0, 30, print1(a(n), ", "))
(PARI) {a(n)=polcoeff( (1-x)^5 / sqrt(1 - 10*x + 33*x^2 - 56*x^3 + 66*x^4 - 54*x^5 + 28*x^6 - 8*x^7 + x^8 +x*O(x^n)), n)}
for(n=0, 30, print1(a(n), ", "))

Crossrefs

Cf. A249946, A249792, A249794.

Sequence in context: A055421 A110213 A034348 * A268990 A005055 A037506

Adjacent sequences: A249790 A249791 A249792 * A249794 A249795 A249796

Keyword

nonn

Author

Paul D. Hanna, Nov 12 2014

Status

approved