A129482 E.g.f.: A(x) = Product_{n>=0} [1 + Sum_{k>=n+1} C(k-1,n)*x^k/k! ].

1, 1, 2, 7, 26, 101, 462, 2528, 15108, 92443, 581138, 3910688, 29024316, 234464634, 1982157166, 17009089378, 147132511520, 1301376431363, 12058326893970, 119068705590380, 1249031077693044, 13641953001474076, 151668261047351986

Offset

0,3

Comments

G.f. for A129483 is closely related.

Links

Table of n, a(n) for n=0..22.

Example

E.g.f.: A(x) = 1 + x + 2x^2/2! + 7x^3/3! + 26x^4/4! +
101x^5/5! +...
Product formula is illustrated by:
A(x) = [1 + x + x^2/2! + x^3/3! + x^4/4! + x^5/5! +...]*
[1 + x^2/2! + 2x^3/3! + 3x^4/4! + 4x^5/5! + 5x^6/6! +...]*
[1 + x^3/3! + 3x^4/4! + 6x^5/5! + 10x^6/6! + 15x^7/7! +...]*
[1 + x^4/4! + 4x^5/5! + 10x^6/6! + 20x^7/7! + 35x^8/8! +...]*
[1 + x^5/5! + 5x^6/6! + 15x^7/7! + 35x^8/8! + 70x^9/9! +...]*...*
[1 + Sum_{k>=n+1} C(k-1,n)*x^k/k! ]*...

Prog

(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)}

Crossrefs

Cf. A129483.

Sequence in context: A045868 A171711 A363293 * A150536 A307413 A326564

Adjacent sequences: A129479 A129480 A129481 * A129483 A129484 A129485

Keyword

nonn

Author

Paul D. Hanna, Apr 17 2007

Status

approved