A294947 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of exp(-Sum_{j>0} sigma_k(j)*x^j/j) in powers of x.

1, 1, -1, 1, -1, -2, 1, -1, -4, -7, 1, -1, -8, -23, -57, 1, -1, -16, -73, -229, -541, 1, -1, -32, -227, -927, -2761, -7126, 1, -1, -64, -697, -3757, -13969, -42615, -108072, 1, -1, -128, -2123, -15207, -70237, -254580, -758499, -1966034

Offset

0,6

Links

Table of n, a(n) for n=0..44.

Formula

G.f. of column k: Product_{j>0} (1 - j^j*x^j)^(j^(k-1)).

Example

Square array begins:
      1,     1,      1,      1,       1, ...
     -1,    -1,     -1,     -1,      -1, ...
     -2,    -4,     -8,    -16,     -32, ...
     -7,   -23,    -73,   -227,    -697, ...
    -57,  -229,   -927,  -3757,  -15207, ...
   -541, -2761, -13969, -70237, -351361, ...

Crossrefs

Columns k=0..2 give A294948, A292312, A294809.

Rows n=0..1 give A000012, (-1)*A000012.

Cf. A294946, A294951.

Sequence in context: A264622 A275017 A141036 * A265232 A011016 A096540

Adjacent sequences: A294944 A294945 A294946 * A294948 A294949 A294950

Keyword

sign,tabl

Author

Seiichi Manyama, Nov 11 2017

Status

approved