A204857 G.f.: Sum_{n>=0} n!*x^(n*(n+1)/2) / Product_{k=1..n} (1 - (n-k+1)*x^k).

1, 1, 1, 3, 5, 11, 27, 61, 151, 375, 1001, 2699, 7635, 22069, 65695, 199671, 620417, 1966715, 6367323, 21059149, 71216311, 246322503, 871268465, 3148964147, 11613253707, 43625643373, 166606282471, 645633978279, 2534590357457, 10066575332603

Offset: 0

Author

Paul D. Hanna, Jan 20 2012

Keywords

• nonn

Examples

			G.f.: A(x) = 1 + x + x^2 + 3*x^3 + 5*x^4 + 11*x^5 + 27*x^6 + 61*x^7 +...
where A(x) = 1 + x/(1-x) + 2!*x^3/((1-2*x)*(1-x^2)) + 3!*x^6/((1-3*x)*(1-2*x^2)*(1-x^3)) + 4!*x^10/((1-4*x)*(1-3*x^2)*(1-2*x^3)*(1-x^4)) +...
		

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..250

Crossrefs

Cf. A204858, A204855.

Programs

Mathematica

Table[SeriesCoefficient[Sum[n!*x^Binomial[n + 1, 2]/Product[(1 - (n - k + 1)*x^k), {k, 1, n}], {n, 0, 100}], {x, 0, n}], {n, 0, 50}] (* G. C. Greubel, Dec 19 2017 *)

PARI

{a(n)=polcoeff(1+sum(m=1,n,m!*x^(m*(m+1)/2)/prod(k=1,m,1-(m-k+1)*x^k+x*O(x^n))),n)}