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A101477 Square array T(n,k), read by antidiagonals: number of labeled trees, with increments of labels along edges constrained to +-1, with n nodes that have no label greater than k. +0
1
1, 1, 1, 1, 2, 3, 1, 2, 7, 12, 1, 2, 8, 31, 56, 1, 2, 8, 39, 156, 288, 1, 2, 8, 40, 211, 851, 1584, 1, 2, 8, 40, 223, 1219, 4909, 9152, 1, 2, 8, 40, 224, 1327, 7371, 29506, 54912, 1, 2, 8, 40, 224, 1343, 8250, 46099, 183043, 339456, 1, 2, 8, 40, 224, 1344, 8427 (list; table; graph; listen)
OFFSET

0,5

LINKS

M. Bousquet-Melou, Limit laws for embedded trees

FORMULA

G.f. of k-th row: A(t)=B(t)*(1-C(t)^(k+1))*(1-C(t)^(k+5))/[(1-C(t)^(k+2))*(1-C(t)^(k+4))], with tB(t) the g.f. of A052701 and C(t) the g.f. of A101478.

EXAMPLE

1,1,3,12,56,288,1584,9152,54912,339456,

1,2,7,31,156,851,4909,29506,183043,1164387,

1,2,8,39,211,1219,7371,46099,295915,1939395,

1,2,8,40,223,1327,8250,52938,347941,2330532,

1,2,8,40,224,1343,8427,54625,362833,2456261,

1,2,8,40,224,1344,8447,54887,365688,2484384,

1,2,8,40,224,1344,8448,54911,366051,2488831,

1,2,8,40,224,1344,8448,54912,366079,2489311,

1,2,8,40,224,1344,8448,54912,366080,2489343,

1,2,8,40,224,1344,8448,54912,366080,2489344,

CROSSREFS

Rows converge to A052701. First row is A000257.

Adjacent sequences: A101474 A101475 A101476 this_sequence A101478 A101479 A101480

Sequence in context: A109091 A138507 A109200 this_sequence A077887 A059379 A065487

KEYWORD

nonn,tabl

AUTHOR

Ralf Stephan, Jan 21 2005

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Last modified October 7 14:39 EDT 2008. Contains 144666 sequences.


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