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A094952
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A sequence derived from pentagonal numbers, or a Stirling number of the first kind matrix.
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1
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6, 35, 105, 234, 440, 741, 1155, 1700, 2394, 3255, 4301, 5550, 7020, 8729, 10695, 12936, 15470, 18315, 21489, 25010, 28896, 33165, 37835, 42924, 48450, 54431, 60885, 67830, 75284, 83265, 91791, 100880, 110550, 120819, 131705, 143226
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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REFERENCES
| R. Aldrovandi, "Special Matrices of Mathematical Physics", World Scientific, 2001, 13.3.1 "Inverting Bell Matrices", p. 171.
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FORMULA
| a(n) = (2n+1)*A005449(n) where A005449 = 2, 7, 15, 26, 40... Given the 4th order Stirling number of the first kind matrix [1 0 0 0 / -1 1 0 0 / 2 -3 1 0 / -6 11 -6 1] = M, M^n * [1 0 0 0] = [1 -n A005449(n) -a(n)]
Empirical G.f.: x*(6+11*x+x^2)/(1-x)^4. [Colin Barker, Jan 14 2012]
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EXAMPLE
| a(5) = 440 = (2n+1)*A005449(n) = 11 * 40.
a(6) = 741 since M^7 * [1 0 0 0] = [1 -6 57 -741].
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MATHEMATICA
| a[n_] := (MatrixPower[{{1, 0, 0, 0}, {-1, 1, 0, 0}, {2, -3, 1, 0}, {-6, 11, -6, 1}}, n].{{1}, {0}, {0}, {0}})[[4, 1]]; Table[ Abs[ a[n]], {n, 36}] (from Robert G. Wilson v Jun 05 2004)
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CROSSREFS
| Cf. A005449.
Sequence in context: A009583 A033578 A101077 * A024526 A089581 A132657
Adjacent sequences: A094949 A094950 A094951 * A094953 A094954 A094955
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KEYWORD
| nonn
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AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com), May 26 2004
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EXTENSIONS
| Edited by Robert G. Wilson v (rgwv(AT)rgwv.com), Jun 05 2004
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