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Search: id:A008955
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| A008955 |
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Triangle of central factorial numbers t(2n,2n-2k) read by rows. |
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+0
13
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| 1, 1, 1, 1, 5, 4, 1, 14, 49, 36, 1, 30, 273, 820, 576, 1, 55, 1023, 7645, 21076, 14400, 1, 91, 3003, 44473, 296296, 773136, 518400, 1, 140, 7462, 191620, 2475473, 15291640, 38402064, 25401600, 1, 204, 16422, 669188, 14739153, 173721912
(list; table; graph; listen)
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OFFSET
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0,5
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COMMENT
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The terms in row n are the coefficients of Prod[i=1..n, x+i^2].
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REFERENCES
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P. A. MacMahon, Divisors of numbers and their continuations in the theory of partitions, Proc. London Math. Soc., (2) 19 (1919), 75-113; Coll. Papers II, pp. 303-341.
J. Riordan, Combinatorial Identities, Wiley, 1968, p. 217.
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LINKS
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T. D. Noe, Rows n=0..50 of triangle, flattened
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FORMULA
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T(n, k) = T(n, k-1) + k^2*T(n-1, k-1) (with a different labeling).
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EXAMPLE
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1; 1,1; 1,5,4; 1,14,49,36; 1,30,273,820,576; ...
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CROSSREFS
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Cf. A036969.
Columns include A000330, A000596, A000597. Right-hand columns include A001044, A001819, A001820, A001821. Row sums are in A101686.
Sequence in context: A072222 A005752 A098494 this_sequence A108440 A102220 A109430
Adjacent sequences: A008952 A008953 A008954 this_sequence A008956 A008957 A008958
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KEYWORD
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tabl,nonn,nice,easy
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AUTHOR
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njas
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EXTENSIONS
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There's an error in the last column of Riordan's table (change 46076 to 21076).
More terms from Vladeta Jovovic (vladeta(AT)Eunet.yu), Apr 16 2000
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