A227467 E.g.f.: exp( Sum_{n>=1} (1+x)^(n^2) * x^n/n ).

1, 1, 4, 24, 252, 3660, 73560, 1921080, 63411600, 2574406800, 125747475840, 7258472907840, 487590023511360, 37629962101892160, 3299990581104497280, 325758967714868688000, 35904380354917794720000, 4387164775718671231084800, 590610815931660911894707200, 87118296156852814044256665600

Offset: 0

Author

Paul D. Hanna, Aug 24 2013

Keywords

• nonn

Comments

Compare the definition to: exp( Sum_{n>=1} (1+y)^(n^2) * x^n/n ), which yields an integer series whenever y is an integer.

Note that exp( Sum_{n>=1} x^n/n * Sum_{k=0..n} binomial(n^2, n*k) * x^k ) yields an integer series (A206830).

Examples

			E.g.f.: A(x) = 1 + x + 4*x^2/2! + 24*x^3/3! + 252*x^4/4! + 3660*x^5/5! +...
where, by definition,
log(A(x)) = (1+x)*x + (1+x)^4*x^2/2 + (1+x)^9*x^3/3 + (1+x)^16*x^4/4 + (1+x)^25*x^5/5+ (1+x)^36*x^6/6+ (1+x)^49*x^7/7 +...
		

Crossrefs

Cf. A206830, A167006.

Programs

PARI

{a(n)=n!*polcoeff(exp(sum(m=1, n, (1+x)^(m^2)*x^m/m)+x*O(x^n)), n)}
for(n=0,25,print1(a(n),", "))