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

Author

Wolfdieter Lang, Jul 28 2017

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A094816, A290311.

Programs

PARI

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

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)