login
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
OFFSET
0,2
COMMENTS
See A094816 and A290311.
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
Sequence in context: A106113 A362153 A299260 * A374974 A028419 A046664
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Jul 28 2017
STATUS
approved