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A163944 Fourth left hand column of triangle A163940. 4
0, 4, 49, 246, 834, 2250, 5214, 10829, 20696, 37044, 62875, 102124, 159834, 242346, 357504, 514875, 725984, 1004564, 1366821, 1831714, 2421250, 3160794, 4079394, 5210121, 6590424, 8262500, 10273679, 12676824, 15530746, 18900634, 22858500 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
FORMULA
G.f.: x*(4 +21*x -13*x^2 +x^3 +3*x^4 -x^5)/(1-x)^7.
a(n) = (10*n^2 +107*n^3 +61*n^4 +13*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).
E.g.f.: (1/48)*x*(192 + 984*x + 888*x^2 + 256*x^3 + 28*x^4 + x^5)*exp(x). - G. C. Greubel, Aug 13 2017
MATHEMATICA
CoefficientList[Series[x*(4 + 21*x - 13*x^2 + x^3 + 3*x^4 - x^5)/(1 - x)^7, {x, 0, 50}], x] (* G. C. Greubel, Aug 13 2017 *)
LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {0, 4, 49, 246, 834, 2250, 5214}, 40] (* Harvey P. Dale, Apr 29 2019 *)
PROG
(PARI) x='x+O('x^50); concat([0], Vec(x*(4 +21*x -13*x^2 +x^3 +3*x^4 -x^5)/(1-x)^7)) \\ G. C. Greubel, Aug 13 2017
CROSSREFS
Cf. A163972.
Equals the fourth left hand column of A163940.
A163943 is another left hand column.
Sequence in context: A295535 A078187 A100256 * A000596 A113525 A290263
KEYWORD
easy,nonn
AUTHOR
Johannes W. Meijer, Aug 13 2009
STATUS
approved

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Last modified June 19 00:22 EDT 2024. Contains 373492 sequences. (Running on oeis4.)