A005194 Number of balanced symmetric graphs. (Formerly M1017)

1, 2, 4, 6, 10, 22, 38, 102, 182, 574, 1070, 3798, 7286, 28894, 57374, 248502, 506678, 2384254, 5007230, 25247958, 54311126, 292500574, 645652574, 3680048502, 8301671798, 49967727934, 115334270270, 728281984278, 1714641313046, 11341092707614

Offset

1,2

References

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Table of n, a(n) for n=1..30.

David A. Sheppard, The factorial representation of balanced labelled graphs, Discrete Math. 15 (1976), no. 4, 379-388.

Formula

Let S(n,j) = j! * j^floor((n-2)/2). If n is even, then a(n) = 2 * Sum_{j=1..n/2} S(n,j). If n is odd, and (n-1)/2 is odd, then a(n) = ((n+1)/2)! + 2 * Sum_{j=1,3,5,...,(n-1)/2} S(n, j). Otherwise, n is odd, and (n-1)/2 is even, then a(n) = ((n+1)/2)! + ((n-1)/2)! + 2 * Sum_{j=1,3,5,...,(n-1)/2-1} S(n, j) [From Sheppard paper]. - Sean A. Irvine, Apr 18 2016

Crossrefs

Sequence in context: A293281 A164143 A095007 * A171447 A207667 A085809

Adjacent sequences: A005191 A005192 A005193 * A005195 A005196 A005197

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Sean A. Irvine, Apr 18 2016

Status

approved