A207571 G.f.: Sum_{n>=0} Product_{k=1..n} ((1+x)^(3*k-1) - 1).

1, 2, 11, 105, 1390, 23520, 484247, 11742927, 327711230, 10343198878, 364237027076, 14156867852699, 601927703437645, 27790427952836499, 1384496764982434033, 74027620787319243688, 4228343290201028904807, 256946673653717460509502, 16551666142815138743519611

Offset

0,2

Comments

Compare g.f. to: Sum_{n>=0} Product_{k=1..n} ((1+x)^k - 1), which is the g.f. of A179525.

Links

Michael De Vlieger, Table of n, a(n) for n = 0..200

Hsien-Kuei Hwang, Emma Yu Jin, Asymptotics and statistics on Fishburn matrices and their generalizations, arXiv:1911.06690 [math.CO], 2019.

Formula

a(n) ~ GAMMA(1/3) * 2^(2*n+1/3) * 3^(2*n+7/6) * n^(n+1/6) / (exp(n+Pi^2/72) * Pi^(2*n+11/6)). - Vaclav Kotesovec, May 06 2014

Example

G.f.: A(x) = 1 + 2*x + 11*x^2 + 105*x^3 + 1390*x^4 + 23520*x^5 + 484247*x^6 +...
such that, by definition,
A(x) = 1 + ((1+x)^2-1) + ((1+x)^2-1)*((1+x)^5-1) + ((1+x)^2-1)*((1+x)^5-1)*((1+x)^8-1) + ((1+x)^2-1)*((1+x)^5-1)*((1+x)^8-1)*((1+x)^11-1) +...

Mathematica

CoefficientList[Series[Sum[Product[(1+x)^(3*k-1)-1, {k, 1, n}], {n, 0, 20}], {x, 0, 20}], x] (* Vaclav Kotesovec, May 06 2014 *)

Prog

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

Crossrefs

Cf. A179525, A207556, A207569, A207570.

Sequence in context: A364338 A379446 A375457 * A351331 A278070 A292428

Adjacent sequences: A207568 A207569 A207570 * A207572 A207573 A207574

Keyword

nonn

Author

Paul D. Hanna, Feb 18 2012

Status

approved