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

0,2

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

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)

Prog

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

Crossrefs

Cf. A094816, A290311, A290312.

Sequence in context: A042116 A215756 A340639 * A042118 A039494 A159650

Adjacent sequences: A290310 A290311 A290312 * A290314 A290315 A290316

Keyword

nonn,easy

Author

Wolfdieter Lang, Jul 28 2017

Status

approved