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A145126
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1 + (6 + (11 + (6 + n)*n)*n)*n/24.
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5
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1, 2, 6, 16, 36, 71, 127, 211, 331, 496, 716, 1002, 1366, 1821, 2381, 3061, 3877, 4846, 5986, 7316, 8856, 10627, 12651, 14951, 17551, 20476, 23752, 27406, 31466, 35961, 40921, 46377, 52361, 58906, 66046, 73816, 82252, 91391, 101271, 111931, 123411
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Contribution from Gary W. Adamson (qntmpkt(AT)yahoo.com), Jul 31 2010: (Start)
Equals (1, 2, 3, 4, 5,...) convolved with (1, 0, 3, 6, 10, 15,...).
Example: a(4) = 36 = (5, 4, 3, 2, 1) dot (1, 0, 3, 6, 10) = (5 + 0 + 9 + 12 + 10). (End)
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FORMULA
| G.f.: (x^4-4*x^3+6*x^2-3*x+1) / (1-x)^5.
a(n)=C(n,4)+1,n>=3 [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 24 2009]
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MAPLE
| a := n-> 1+ (6+ (11+ (6+ n) *n) *n) *n/24: seq (a(n), n=0..40);
with(combinat):seq(binomial(n, 4)+1, n=3..43); #) [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 24 2009]
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MATHEMATICA
| a=b=s=0; lst={a}; Do[a+=n; b+=a; s+=b; AppendTo[lst, s], {n, 6!}]; lst+1 [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Jun 14 2009]
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CROSSREFS
| 5th row of A145153. See row 5 of A145140/A145141 for rational coefficients and A145142 for 24 * coefficients of polynomial.
Sequence in context: A060354 A140131 A159938 * A005676 A038503 A079990
Adjacent sequences: A145123 A145124 A145125 * A145127 A145128 A145129
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KEYWORD
| nonn
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AUTHOR
| Alois P. Heinz (heinz(AT)hs-heilbronn.de), Oct 03 2008
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