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A168246 Inverse Weigh transform of n!. 5
1, 2, 4, 19, 92, 576, 4156, 34178, 314368, 3199936, 35703996, 433422071, 5687955724, 80256879068, 1211781887796, 19496946568898, 333041104402860, 6019770247224496, 114794574818830716, 2303332661419442569, 48509766592884311132, 1069983257387168051076 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..449

FORMULA

Product_{k>=1} (1+x^k)^a(k) = Sum_{n>=0} n! x^n.

MAPLE

b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,

      add(binomial(a(i), j)*b(n-i*j, i-1), j=0..n/i)))

    end:

a:= proc(n) option remember; n! -b(n, n-1) end:

seq(a(n), n=1..30);  # Alois P. Heinz, Jun 11 2018

PROG

(PARI) seq(n)={dirdiv(Vec(log(1+x*Ser(vector(n, n, n!)))), -vector(n, n, (-1)^n/n))} \\ Andrew Howroyd, Jun 22 2018

CROSSREFS

Cf. A000142, A112354, A261052 (Weigh transform of n!).

Sequence in context: A226891 A289269 A272988 * A212923 A058130 A191563

Adjacent sequences:  A168243 A168244 A168245 * A168247 A168248 A168249

KEYWORD

easy,nonn

AUTHOR

Vladeta Jovovic, Nov 21 2009

STATUS

approved

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Last modified September 19 01:08 EDT 2018. Contains 315153 sequences. (Running on oeis4.)