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A132164
Row sums of triangle A134141 (S1p(7)).
4
1, 1, 8, 78, 918, 12846, 209616, 3909228, 81859548, 1897344828, 48135826656, 1325008302696, 39292978029768, 1247949491330088, 42236558731574208, 1516738194700667856, 57573649342673292816, 2302425590703685075728, 96720470167595138898048
OFFSET
0,3
LINKS
FORMULA
a(n)= sum(A134141(n,m),m=1..n),n>=1.
E.g.f.: exp((1-(1-x)^6)/(6*(1-x)^6)). Cf. e.g.f. first column of A134141.
From Seiichi Manyama, Jan 18 2025: (Start)
a(n) = Sum_{k=0..n} |Stirling1(n,k)| * A005012(k).
a(n) = (1/exp(1/6)) * (-1)^n * n! * Sum_{k>=0} binomial(-6*k,n)/(6^k * k!). (End)
MAPLE
a:= proc(n) option remember; `if`(n=0, 1, add(
binomial(n-1, j-1)*(j+5)!/6!*a(n-j), j=1..n))
end:
seq(a(n), n=0..25); # Alois P. Heinz, Aug 01 2017
MATHEMATICA
a[n_]:=a[n]=If[n==0, 1, Sum[Binomial[n - 1, j - 1] (j + 5)!/6! a[n - j], {j, n}]]; Table[a[n], {n, 0, 25}] (* Indranil Ghosh, Aug 02 2017, after Maple code *)
CROSSREFS
Cf. A132165 (alternating row sum of A134141), A049428.
Sequence in context: A199758 A111533 A218499 * A058480 A000435 A052698
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Oct 12 2007
EXTENSIONS
a(0)=1 prepended by Alois P. Heinz, Aug 01 2017
STATUS
approved