A230050 G.f.: Sum_{n>=0} x^n / (1-x)^(n^3).

1, 1, 2, 10, 65, 564, 6191, 82050, 1295263, 23764278, 499547080, 11892550569, 317112508944, 9392408105655, 306739296397827, 10973970687363844, 427724034697254939, 18073023112616933860, 824247511186225346295, 40415810147764633887442, 2123162727678797736474583

Offset

0,3

Links

Table of n, a(n) for n=0..20.

Formula

a(n) = Sum_{k=0..n} binomial(k^3 + n-k-1, n-k).

Equals row sums of triangle A230049.

Example

G.f.: A(x) = 1 + x + 2*x^2 + 10*x^3 + 65*x^4 + 564*x^5 + 6191*x^6 + 82050*x^7 +...
where
A(x) = 1 + x/(1-x) + x^2/(1-x)^8 + x^3/(1-x)^27 + x^4/(1-x)^64 + x^5/(1-x)^125 + x^6/(1-x)^216 + x^7/(1-x)^343 +...

Prog

(PARI) {a(n)=polcoeff(sum(k=0, n, x^k/(1-x+x*O(x^n))^(k^3)), n)}
for(n=0, 25, print1(a(n), ", "))
(PARI) {a(n)=sum(k=0, n, binomial(k^3+n-k-1, n-k))}
for(n=0, 25, print1(a(n), ", "))

Crossrefs

Cf. A230049, A178325, A227934, A227935.

Sequence in context: A167449 A064170 A151410 * A340467 A278459 A278461

Adjacent sequences: A230047 A230048 A230049 * A230051 A230052 A230053

Keyword

nonn

Author

Paul D. Hanna, Oct 06 2013

Status

approved