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A350635
Triangle read by rows: T(n,k) is the number of n-element unlabeled P-series with k connected components.
1
1, 1, 1, 3, 1, 1, 7, 4, 1, 1, 15, 10, 4, 1, 1, 31, 28, 11, 4, 1, 1, 63, 67, 31, 11, 4, 1, 1, 127, 167, 80, 32, 11, 4, 1, 1, 255, 388, 213, 83, 32, 11, 4, 1, 1, 511, 908, 534, 226, 84, 32, 11, 4, 1, 1, 1023, 2053, 1343, 580, 229, 84, 32, 11, 4, 1, 1
OFFSET
1,4
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..1275 (rows 1..50)
FORMULA
G.f.: -1 + exp(Sum_{k>=1} y^k*B(x^k)/k) where B(x) = x*(1 - 2*x + 2*x^2)/((1 - x)*(1 - 2*x)). - Andrew Howroyd, Jan 13 2022
EXAMPLE
Triangle begins:
1;
1, 1;
3, 1, 1;
7, 4, 1, 1;
15, 10, 4, 1, 1;
31, 28, 11, 4, 1, 1;
63, 67, 31, 11, 4, 1, 1;
127, 167, 80, 32, 11, 4, 1, 1;
...
PROG
(PARI)
B(x) = x*(1 - 2*x + 2*x^2)/((1 - x)*(1 - 2*x))
T(n)=[Vecrev(p/y) | p<-Vec(-1 + exp(sum(k=1, n, y^k*B(x^k)/k + O(x*x^n))))]
{ my(A=T(8)); for(n=1, #A, print(A[n])) } \\ Andrew Howroyd, Jan 13 2022
CROSSREFS
Row sums give A349276.
Column 1 is A255047(n-1).
Cf. A263864 (all posets), A349488 (disconnected).
Sequence in context: A309402 A135288 A078026 * A126713 A140068 A179745
KEYWORD
nonn,tabl
AUTHOR
STATUS
approved