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

1,2

Links

Table of n, a(n) for n=1..30.

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

Adjacent sequences: A133707 A133708 A133709 * A133711 A133712 A133713

Keyword

nonn

Author

N. J. A. Sloane, Dec 30 2007

Extensions

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

Status

approved