A290313 Fourth diagonal sequence of the Sheffer triangle A094816 (special Charlier).

1, 24, 145, 545, 1575, 3836, 8274, 16290, 29865, 51700, 85371, 135499, 207935, 309960, 450500, 640356, 892449, 1222080, 1647205, 2188725, 2870791, 3721124, 4771350, 6057350, 7619625, 9503676, 11760399, 14446495, 17624895, 21365200, 25744136, 30846024, 36763265, 43596840, 51456825, 60462921, 70744999, 82443660, 95710810, 110710250

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 (7,-21,35,-35,21,-7,1).

Crossrefs

Cf. A094816, A290311, A290312.

Programs

PARI

Vec((1 + 17*x - 2*x^2 - x^3) / (1 - x)^7 + O(x^50)) \\ Colin Barker, Jul 29 2017

Formula

O.g.f: (1 + 17*x - 2*x^2 - x^3)/(1 - x)^7.

E.g.f.: exp(x)*(1 + 23*x + 98*x^2/2! + 181*x^3/3! + 170*x^4/4! + 80*x^5/5! + 15*x^6/6!).

From Colin Barker, Jul 29 2017: (Start)

a(n) = (48 + 256*n + 422*n^2 + 303*n^3 + 105*n^4 + 17*n^5 + n^6) / 48.

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 > 6.

(End)