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A081114 Triangle read by rows of T(n,k)=n*T(n-1,k)+n-k starting at T(n,n)=0. 0
0, 1, 0, 4, 1, 0, 15, 5, 1, 0, 64, 23, 6, 1, 0, 325, 119, 33, 7, 1, 0, 1956, 719, 202, 45, 8, 1, 0, 13699, 5039, 1419, 319, 59, 9, 1, 0, 109600, 40319, 11358, 2557, 476, 75, 10, 1, 0, 986409, 362879, 102229, 23019, 4289, 679, 93, 11, 1, 0, 9864100, 3628799, 1022298 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Taking the triangle into negative values of n and k would produce results close to (k+1)*e*n! - 1, i.e. one less than multiples of A000522 for nonnegative n.

LINKS

Table of n, a(n) for n=0..57.

FORMULA

For k>0, T(n, k)=ceiling[ (A001339(k-1)/(k-1)! - (k-1)*e) *n! - 1] where A001339(k-1)=ceiling[(k-1)!*(k-1)*e for k>1]. T(n, 0)=floor[e*n! - 1] for n>0; T(n, 1)=n!-1. T(n, n)=0; T(n, n-1)=n+2; T(n, n-2)=n^2+3n+5=A027688(n+1).

EXAMPLE

Rows start: 0; 1,0; 4,1,0; 15,5,1,0; 64,23,6,1,0; 325,119,33,7,1,0; etc.

CROSSREFS

Columns include A007526 and A033312.

Sequence in context: A060638 A244125 A007789 * A069018 A156811 A246609

Adjacent sequences:  A081111 A081112 A081113 * A081115 A081116 A081117

KEYWORD

nonn,tabl

AUTHOR

Henry Bottomley, Apr 16 2003

STATUS

approved

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Last modified November 16 22:10 EST 2018. Contains 317275 sequences. (Running on oeis4.)