A081913 a(n) = 2^n*(n^3 - 3*n^2 + 2*n + 48)/48.

1, 2, 4, 9, 24, 72, 224, 688, 2048, 5888, 16384, 44288, 116736, 301056, 761856, 1896448, 4653056, 11272192, 27000832, 64028672, 150470656, 350748672, 811597824, 1865416704, 4261412864, 9680453632, 21877489664, 49207574528, 110192754688, 245752659968, 545997717504

Offset

0,2

Comments

Binomial transform of A050407, (starting with 1,1,1,2,5,...). 2nd binomial transform of (1,0,0,1,0,0,0,0,...). Case k=2 where a(n,k) = k^n*(n^3 - 3*n^2 + 2*n + 6*k^3)/(6*k^3), with g.f. (1 - 3*k*x + 3*k^2*x^2 - (k^3-1)*x^3)/(1-k*x)^4.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..225

Index entries for linear recurrences with constant coefficients, signature (8,-24,32,-16).

Formula

a(n) = 2^n*(n^3 - 3*n^2 + 2*n + 48)/48.

G.f.: (1 - 6*x + 12*x^2 - 7*x^3)/(1-2*x)^4.

From Elmo R. Oliveira, Nov 13 2025: (Start)

E.g.f.: (1 + x^3/6)*exp(2*x).

a(n) = 8*a(n-1) - 24*a(n-2) + 32*a(n-3) - 16*a(n-4). (End)

Prog

(Magma) [2^n*(n^3-3*n^2+2*n+48)/48: n in [0..40]]; // Vincenzo Librandi, Apr 27 2011

Crossrefs

Cf. A050407, A081914.

Sequence in context: A200966 A148084 A156804 * A092236 A367112 A336023

Adjacent sequences: A081910 A081911 A081912 * A081914 A081915 A081916

Keyword

easy,nonn

Author

Paul Barry, Mar 31 2003

Status

approved