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A133710
Column l=3 of irregular triangle in A133709.
3
0, 3, 35, 131, 347, 767, 1511, 2744, 4686, 7623, 11919, 18029, 26513, 38051, 53459, 73706, 99932, 133467, 175851, 228855, 294503, 375095, 473231, 591836, 734186, 903935, 1105143, 1342305, 1620381, 1944827
OFFSET
1,2
FORMULA
Conjectures from Colin Barker, Apr 03 2020: (Start)
G.f.: x^2*(3 + 14*x - 51*x^2 + 60*x^3 - 31*x^4 + 6*x^5) / (1 - x)^7.
a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.
(End)
MAPLE
A133710 := proc(m)
A133709(m, 3) ;
end proc:
seq(A133710(m), m=1..30) ; # R. J. Mathar, Nov 23 2011
MATHEMATICA
T[m_, l_] := T[m, l] = If[l == 1, 1, Sum[(-1)^i Binomial[l, i]* Binomial[2^(l - i) + m - 2, m], {i, 0, l - 1}] - Sum[StirlingS2[l, i]* T[m, i], {i, 1, l - 1}]];
Table[T[m, 3], {m, 1, 30}] (* Jean-François Alcover, Apr 03 2020 *)
CROSSREFS
Cf. A133709.
Sequence in context: A076376 A338787 A353619 * A130061 A368391 A274875
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Dec 30 2007
EXTENSIONS
Typo in data corrected by Jean-François Alcover, Apr 03 2020
STATUS
approved