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A193450
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Triangle of a binomial convolution sum related to Jacobsthal numbers.
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2
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0, 1, 0, 2, 2, 2, 3, 6, 6, 0, 4, 12, 16, 8, 4, 5, 20, 35, 30, 15, 0, 6, 30, 66, 78, 54, 18, 6, 7, 42, 112, 168, 154, 84, 28, 0, 8, 56, 176, 320, 368, 272, 128, 32, 8, 9, 72, 261, 558, 774, 720, 450, 180, 45, 0, 10, 90, 370, 910, 1480, 1660, 1300, 700, 250, 50, 10
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listen;
history;
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OFFSET
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0,4
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COMMENTS
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Row sum is A193449(n) = A001045(n+1)*n.
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LINKS
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Table of n, a(n) for n=0..65.
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FORMULA
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T(n,k) = sum( (-1)^j*n*C(n-j,k-j), j=0..k).
T(n,k) = n*C(n, k)*2F1( (1, -k); -n )(-1).
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EXAMPLE
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Triangle starts:
0;
1, 0;
2, 2, 2;
3, 6, 6, 0;
4, 12, 16, 8, 4;
5, 20, 35, 30, 15, 0;
...
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PROG
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(PARI) T(n, k) = sum(j=0, k, (-1)^j*n*binomial(n-j, k-j)); \\ Michel Marcus, Jun 04 2014
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CROSSREFS
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Cf. A193451.
Sequence in context: A104346 A318238 A341075 * A109906 A104856 A306393
Adjacent sequences: A193447 A193448 A193449 * A193451 A193452 A193453
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KEYWORD
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nonn,easy,tabl
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AUTHOR
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Olivier Gérard, Jul 26 2011
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STATUS
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approved
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