A091347 a(n) = 6*4^n - 12*3^n + 7*2^n - 1.

0, 1, 15, 115, 675, 3451, 16275, 72955, 316275, 1340251, 5590035, 23054395, 94314675, 383578651, 1553331795, 6270493435, 25253701875, 101530450651, 407669649555, 1635323974075, 6555235693875, 26262769508251, 105176572911315, 421082805640315, 1685460823266675, 6745232212623451

Offset

0,3

Links

Bruce Nye, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (10,-35,50,-24).

Formula

a(n) = Sum_{i=1..n} i!*i^3*Stirling2(n,i)*(-1)^(n-i).

From Elmo R. Oliveira, May 08 2026: (Start)

G.f.: x*(1 + 5*x) / ((1-x)*(1-2*x)*(1-3*x)*(1-4*x)).

E.g.f.: exp(x)*(6*exp(3*x) - 12*exp(2*x) + 7*exp(x) - 1).

a(n) = 10*a(n-1) - 35*a(n-2) + 50*a(n-3) - 24*a(n-4).

a(n) = A162723(n+1) - 1. (End)

Mathematica

Table[6*4^n - 12*3^n + 7*2^n - 1, {n, 0, 25}]

Prog

(PARI) a(n) = sum(i=1, n, i!*i^3*stirling(n, i, 2)*(-1)^(n-i)); \\ Michel Marcus, Oct 21 2022

Crossrefs

Cf. A091344, A091348, A162723.

Sequence in context: A113527 A044728 A394552 * A125352 A126510 A328725

Adjacent sequences: A091344 A091345 A091346 * A091348 A091349 A091350

Keyword

easy,nonn

Author

Mario Catalani (mario.catalani(AT)unito.it), Jan 03 2004

Extensions

More terms from Michel Marcus, Oct 21 2022

Status

approved