The On-Line Encyclopedia of Integer Sequences (OEIS)

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A135751

E.g.f.: A(x) = 1 + Sum_{n>=1} (1/n!)*Product_{k=1..n} -log(1 - kx).
(history; published version)

#2 by Russ Cox at Fri Mar 30 18:37:07 EDT 2012

AUTHOR

_Paul D. Hanna (pauldhanna(AT)juno.com), _, Nov 27 2007

Discussion

Fri Mar 30

18:37

OEIS Server: https://oeis.org/edit/global/213

#1 by N. J. A. Sloane at Sun Dec 09 03:00:00 EST 2007

NAME

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

DATA

1, 1, 3, 17, 154, 2024, 36188, 841196, 24583200, 880119000, 37813650672, 1917155945616, 113110111375776, 7674684562897728, 592864081434168672, 51688751369089356864, 5047456043997923498496, 548361788269165389069312

OFFSET

0,3

EXAMPLE

E.g.f.: A(x) = 1 + x + 3x^2/2! + 17x^3/3! + 154x^4/4! +2024x^5/5! +...

A(x) = 1 - log(1-x) + log(1-x)*log(1-2x)/2! - log(1-x)*log(1-2x)*log(1-3x)/3! +...

PROG

(PARI) {a(n)=n!*polcoeff(1+sum(j=1, n, (1/j!)*prod(k=1, j, -log(1-k*x +x*O(x^n)))), n)}

KEYWORD

nonn,new

AUTHOR

Paul D. Hanna (pauldhanna(AT)juno.com), Nov 27 2007

STATUS

approved