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A290313 Fourth diagonal sequence of the Sheffer triangle A094816 (special Charlier). 3
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 (list; graph; refs; listen; history; text; internal format)
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: A158047 A042116 A215756 * A042118 A039494 A159650

Adjacent sequences:  A290310 A290311 A290312 * A290314 A290315 A290316

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Jul 28 2017

STATUS

approved

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Last modified January 24 16:34 EST 2020. Contains 331207 sequences. (Running on oeis4.)