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A136396
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1+n*(n+1)*(n^2-n+12)/12.
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2
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1, 3, 8, 19, 41, 81, 148, 253, 409, 631, 936, 1343, 1873, 2549, 3396, 4441, 5713, 7243, 9064, 11211, 13721, 16633, 19988, 23829, 28201, 33151, 38728, 44983, 51969, 59741, 68356, 77873, 88353, 99859, 112456, 126211, 141193, 157473, 175124, 194221, 214841, 237063, 260968, 286639
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Equals antidiagonal sums of the array A179000.
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
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FORMULA
| A007318 * [1,2,3,2,0,0,0...]: Binomial transform of [1, 2, 3, 3, 2, 0, 0, 0,...].
Narayana transform of [1,2,1,0,0,0,...]: (A001263) * [1, 2, 1, 0, 0, 0,...].
G.f. ( -1+2*x-3*x^2+x^3-x^4 ) / (x-1)^5. - R. J. Mathar, Jan 05 2011
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EXAMPLE
| a(3) = 19 = (1, 3, 3, 1) dot (1, 2, 3, 3) = (1 + 6 + 9 + 3).
a(3) = 19 = (1, 6, 6, 1) dot (1, 2, 1, 0) = (1 + 12 + 6 + 0), where (1, 6, 6, 1) = row 4 of the Narayana triangle (A001263).
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MAPLE
| A136396 := proc(n) 1+n*(n+1)*(n^2-n+12)/12 ; end proc:
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CROSSREFS
| Cf. A001263, A179000
Sequence in context: A007326 A067332 A082535 * A006380 A182818 A095846
Adjacent sequences: A136393 A136394 A136395 * A136397 A136398 A136399
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KEYWORD
| nonn,easy
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AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com), Dec 29 2007
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