A133710 Column l=3 of irregular triangle in A133709.

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

Author

N. J. A. Sloane, Dec 30 2007

Keywords

• nonn

Crossrefs

Cf. A133709.

Programs

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 *)

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)

Extensions

Typo in data corrected by Jean-François Alcover, Apr 03 2020