A129482 - OEIS

%I #3 Mar 30 2012 18:37:03

%S 1,1,2,7,26,101,462,2528,15108,92443,581138,3910688,29024316,

%T 234464634,1982157166,17009089378,147132511520,1301376431363,

%U 12058326893970,119068705590380,1249031077693044,13641953001474076,151668261047351986

%N E.g.f.: A(x) = Product_{n>=0} [1 + Sum_{k>=n+1} C(k-1,n)*x^k/k! ].

%C G.f. for A129483 is closely related.

%e E.g.f.: A(x) = 1 + x + 2x^2/2! + 7x^3/3! + 26x^4/4! +

%e 101x^5/5! +...

%e Product formula is illustrated by:

%e A(x) = [1 + x + x^2/2! + x^3/3! + x^4/4! + x^5/5! +...]*

%e [1 + x^2/2! + 2x^3/3! + 3x^4/4! + 4x^5/5! + 5x^6/6! +...]*

%e [1 + x^3/3! + 3x^4/4! + 6x^5/5! + 10x^6/6! + 15x^7/7! +...]*

%e [1 + x^4/4! + 4x^5/5! + 10x^6/6! + 20x^7/7! + 35x^8/8! +...]*

%e [1 + x^5/5! + 5x^6/6! + 15x^7/7! + 35x^8/8! + 70x^9/9! +...]*...*

%e [1 + Sum_{k>=n+1} C(k-1,n)*x^k/k! ]*...

%o (PARI) {a(n)=n!*polcoeff(prod(k=0,n,1+sum(i=1,n-k+1,binomial(k+i-1,k)*x^(k+i)/(k +i)! +x*O(x^n))),n)}

%Y Cf. A129483.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Apr 17 2007