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A076571 Binomial triangle based on factorials. 5
1, 1, 2, 2, 3, 5, 6, 8, 11, 16, 24, 30, 38, 49, 65, 120, 144, 174, 212, 261, 326, 720, 840, 984, 1158, 1370, 1631, 1957, 5040, 5760, 6600, 7584, 8742, 10112, 11743, 13700, 40320, 45360, 51120, 57720, 65304, 74046, 84158, 95901, 109601, 362880, 403200 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..46.

E. Biondi, L. Divieti, G. Guardabassi, Counting paths, circuits, chains and cycles in graphs: A unified approach, Canad. J. Math. 22 1970 22-35. See Table I.

D. Dumont, Matrices d'Euler-Seidel, Sem. Loth. Comb. B05c (1981) 59-78.

FORMULA

T(n, k) =Sum_i{0<=i<=k}C(k, i)*(n-i)! =T(n, k-1)+T(n-1, k-1) with T(n, 0)=n!.

EXAMPLE

Rows start:

1;

1,2;

2,3,5;

6,8,11,16;

24,30,38,49,65;

120,144,174,212,261,326;

etc.

CROSSREFS

Columns include A000142, A001048, A001344, A001345, A001346, A001347. Right hand columns include A000522, A001339, A001340, A001341, A001342. Rows sums are A002627 (offset).

Sequence in context: A118399 A278298 A178927 * A084783 A265853 A129838

Adjacent sequences:  A076568 A076569 A076570 * A076572 A076573 A076574

KEYWORD

nonn,tabl

AUTHOR

Henry Bottomley, Oct 19 2002

STATUS

approved

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Last modified February 19 04:00 EST 2020. Contains 332034 sequences. (Running on oeis4.)