A207648 Expansion of e.g.f. Sum_{n>=0} 1/(n+1)! * Product_{k=1..n} ((1+x)^(n+k) - 1).

1, 1, 5, 60, 1192, 34790, 1378380, 70445130, 4478636736, 344722776048, 31454679473280, 3345722335272240, 409180573835161920, 56883771843543627840, 8902319140111902785280, 1555438839901675382253600, 301239031844599064651635200, 64260075520580099615272097280

Offset

0,3

Comments

Compare e.g.f. to: Sum_{n>=0} 1/(n+1)! * Product_{k=1..n} (n+k)*x, which is a g.f. of Catalan numbers (A000108).

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..275

Formula

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

Example

E.g.f.: A(x) = 1 + x + 5*x^2/2! + 60*x^3/3! + 1192*x^4/4! + 34790*x^5/5! +...
such that, by definition,
A(x) = 1 + ((1+x)^2-1)/2! + ((1+x)^3-1)*((1+x)^4-1)/3! + ((1+x)^4-1)*((1+x)^5-1)*((1+x)^6-1)/4! + ((1+x)^5-1)*((1+x)^6-1)*((1+x)^7-1)*((1+x)^8-1)/5! +...

Prog

(PARI) {a(n)=n!*polcoeff(sum(m=0, n, 1/(m+1)!*prod(k=1, m, (1+x)^(m+k)-1 +x*O(x^n)) ), n)}
for(n=0, 25, print1(a(n), ", "))

Crossrefs

Cf. A207649.

Sequence in context: A113665 A147585 A138215 * A349883 A010793 A180614

Adjacent sequences: A207645 A207646 A207647 * A207649 A207650 A207651

Keyword

nonn

Author

Paul D. Hanna, Feb 19 2012

Status

approved