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A290312 Third diagonal sequence of the Sheffer triangle A094816 (special Charlier). 4
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 (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 (5,-10,10,-5,1).

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)

PROG

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

CROSSREFS

Cf. A094816, A290311.

Sequence in context: A100178 A106113 A299260 * A028419 A046664 A055536

Adjacent sequences:  A290309 A290310 A290311 * A290313 A290314 A290315

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Jul 28 2017

STATUS

approved

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Last modified December 13 06:26 EST 2019. Contains 329968 sequences. (Running on oeis4.)