OFFSET
0,7
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..1325
FORMULA
Column-wise binomial transform of A327377.
E.g.f.: exp(x + U(x,y) + B(x*(1-y) + R(x,y))), where R(x,y) is the e.g.f. of A055302, U(x,y) is the e.g.f. of A055314 and B(x) + x is the e.g.f. of A059167. - Andrew Howroyd, Oct 05 2019
EXAMPLE
Triangle begins:
1
1 0
1 0 1
2 0 6 0
15 12 30 4 3
314 320 260 80 50 0
13757 10890 5445 1860 735 66 15
MATHEMATICA
Table[Length[Select[Subsets[Subsets[Range[n], {2}]], Count[Length/@Split[Sort[Join@@#]], 1]==k&]], {n, 0, 5}, {k, 0, n}]
PROG
(PARI)
my(R=sum(n=1, n, x^n*sum(k=1, n, stirling(n-1, n-k, 2)*y^k/k!)) + O(x*x^n));
my(U=sum(n=2, n, x^n*sum(k=1, n, stirling(n-2, n-k, 2)*y^k/k!)) + O(x*x^n));
my(B=x^2/2 + log(sum(k=0, n, 2^binomial(k, 2)*(x*exp(-x + O(x^n)))^k/k!)));
my(A=exp(x + U + subst(B-x, x, x*(1-y) + R)));
Vecrev(n!*polcoef(A, n), n + 1);
}
{ for(n=0, 8, print(Row(n))) } \\ Andrew Howroyd, Oct 05 2019
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Gus Wiseman, Sep 04 2019
EXTENSIONS
Terms a(28) and beyond from Andrew Howroyd, Sep 09 2019
STATUS
approved