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Search: id:A114496
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| A114496 |
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Sum of binomial(n,k)*binomial(2n+k,k) over all k. |
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+0
6
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| 1, 4, 26, 190, 1462, 11584, 93536, 765314, 6323270, 52638760, 440815036, 3709445084, 31340292076, 265683004240, 2258793820988, 19251776923210, 164440378882630, 1407266585304760, 12063701803046300, 103571977632247076
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Modification of A001850 inspired by the Ap\'ery numbers A005259.
Contribution from Paul Barry (pbarry(AT)wit.ie), Feb 17 2009: (Start)
Central coefficient of (1+4x+5x^2+2x^3)^n. The coefficients are the 4th row of A029635.
The third row of A029635 corresponds to the central Delannoy numbers A001850. (End)
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FORMULA
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Sum(binomial(n, k)*binomial(2n+k, k), k=0..n)
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MATHEMATICA
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Sum[Binomial[n, k]*Binomial[2n+k, k], {k, 0, n}]
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CROSSREFS
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Cf. A114497, A114498.
Cf.: A156886. [From Paul Barry (pbarry(AT)wit.ie), Feb 17 2009]
Sequence in context: A107649 A052763 A084211 this_sequence A127086 A141381 A118971
Adjacent sequences: A114493 A114494 A114495 this_sequence A114497 A114498 A114499
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KEYWORD
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easy,nonn
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AUTHOR
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Eric S Rowland (erowland(AT)math.rutgers.edu), Dec 01 2005
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