A098437 Row sums in triangle of 3rd central factorial numbers (A098436).

1, 2, 11, 111, 1732, 41153, 1361023, 59661972, 3400514643, 244686040585, 21672428066346, 2327934086035165, 299095824104595685, 45325168774732866658, 8011977427652269129031

Offset: 0

Author

Ralf Stephan, Sep 08 2004

Keywords

• nonn

Links

• John Riordan, Letter, Apr 28 1976.

Programs

PARI

{a(n)=polcoeff(sum(m=0, n, x^m/prod(k=1,m+1,1-k^3*x +x*O(x^n))), n)} /* Paul D. Hanna, Feb 15 2012 */

Formula

O.g.f.: Sum_{n>=0} x^n / Product_{k=1..n+1} (1-k^3*x). [From Paul D. Hanna, Feb 15 2012]

G.f.: (1 - G(0) )/(1-x) where G(k) =1 - 1/(1 - x*k^3)/(1-x/(x-1/G(k+1) )); (recursively defined continued fraction). - Sergei N. Gladkovskii, Jan 17 2013