A290312 Third diagonal sequence of the Sheffer triangle A094816 (special Charlier).

1, 8, 29, 75, 160, 301, 518, 834, 1275, 1870, 2651, 3653, 4914, 6475, 8380, 10676, 13413, 16644, 20425, 24815, 29876, 35673, 42274, 49750, 58175, 67626, 78183, 89929, 102950, 117335, 133176, 150568, 169609, 190400, 213045, 237651, 264328, 293189, 324350, 357930

Offset

0,2

Comments

See A094816 and A290311.

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Formula

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

E.g.f.: exp(x)*(1 + 7*x + 14*x^2/2! + 11*x^3/3! + 3*x^4/4!). This is computed from the o.g.f. with eqs. (23)-(25) of the Wolfdieter Lang 2017 link in A282629.

From Colin Barker, Jul 29 2017: (Start)

a(n) = (24 + 70*n + 69*n^2 + 26*n^3 + 3*n^4) / 24.

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n > 4.

(End)

Prog

(PARI) Vec((1 + 3*x - x^2)/(1 - x)^5 + O(x^60)) \\ Colin Barker, Jul 29 2017

Crossrefs

Cf. A094816, A290311.

Sequence in context: A106113 A362153 A299260 * A028419 A046664 A333510

Adjacent sequences: A290309 A290310 A290311 * A290313 A290314 A290315

Keyword

nonn,easy

Author

Wolfdieter Lang, Jul 28 2017

Status

approved