A249637 G.f.: Sum_{n>=0} x^n / Product_{k=n*(n-1)/2+1..n*(n+1)/2} (1 - k*x).

1, 1, 2, 7, 36, 252, 2278, 25479, 343318, 5455963, 100504720, 2117265242, 50438185262, 1345840435641, 39899564488618, 1305139816260887, 46817884128344164, 1831903983379048308, 77815287718736660334, 3573159363560866942735, 176687138080525842904446, 9376097634171921557906827

Offset

0,3

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..310

Example

G.f.: A(x) = 1 + x + 2*x^2 + 7*x^3 + 36*x^4 + 252*x^5 + 2278*x^6 +...
where
A(x) = 1 + x/(1-x) + x^2/((1-2*x)*(1-3*x)) + x^3/((1-4*x)*(1-5*x)*(1-6*x)) + x^4/((1-7*x)*(1-8*x)*(1-9*x)*(1-10*x)) + x^5/((1-11*x)*(1-12*x)*(1-13*x)*(1-14*x)*(1-15*x)) +...

Prog

(PARI) {a(n)=polcoeff(sum(m=0, n, x^m/prod(k=m*(m-1)/2+1, m*(m+1)/2, 1-k*x +x*O(x^n))), n)}
for(n=0, 30, print1(a(n), ", "))

Crossrefs

Sequence in context: A125033 A034430 A143805 * A259793 A112293 A090352

Adjacent sequences: A249634 A249635 A249636 * A249638 A249639 A249640

Keyword

nonn

Author

Paul D. Hanna, Nov 02 2014

Status

approved