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A290314 Fifth diagonal sequence of the Sheffer triangle A094816 (special Charlier). 2
1, 89, 814, 4179, 15659, 47775, 125853, 296703, 641058, 1290718, 2451449, 4432792, 7686042, 12851762, 20818302, 32792898, 50387031, 75717831, 111527416, 161322161, 229533997, 321705945, 444704195, 606959145, 818737920, 1092450996, 1442995659, 1888139134, 2448944324, 3150241204, 4021147020, 5095638548 (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 (9,-36,84,-126,126,-84,36,-9,1).

FORMULA

O.g.f.: (1  + 80*x + 49*x^2 - 27*x^3 + 2*x^4)/(1-x)^9.

E.g.f: exp(x)*(1 + 88*x + 637*x^2/2! + 2003*x^3/3! + 3472*x^4/4! + 3574*x^5/5! + 2185*x^6/6! + 735*x^7/7! + 105*x^8/8!).

From Colin Barker, Jul 29 2017: (Start)

a(n) = (5760 + 67248*n + 158180*n^2 + 161700*n^3 + 87695*n^4 + 26952*n^5 + 4670*n^6 + 420*n^7 + 15*n^8) / 5760.

a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>8.

(End)

PROG

(PARI) Vec((1 + 80*x + 49*x^2 - 27*x^3 + 2*x^4) / (1 - x)^9 + O(x^50)) \\ Colin Barker, Jul 29 2017

CROSSREFS

Cf. A094816, A290311, A290312, A290313.

Sequence in context: A069764 A053580 A239719 * A103548 A241700 A097155

Adjacent sequences:  A290311 A290312 A290313 * A290315 A290316 A290317

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Jul 28 2017

STATUS

approved

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Last modified January 17 15:12 EST 2020. Contains 330958 sequences. (Running on oeis4.)