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Search: id:A101516
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| A101516 |
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Antidiagonal sums of symmetric square array A101515, and also equals the binomial transform of a sequence formed from terms of A101514 repeated twice. |
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+0
3
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| 1, 2, 4, 8, 17, 38, 91, 232, 632, 1824, 5571, 17892, 60355, 212898, 784416, 3008480, 11997341, 49612426, 212536067, 941213428, 4305049140, 20302469824, 98641434683, 493038167880, 2533414749409, 13366134856170, 72361098996208
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OFFSET
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0,2
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COMMENT
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A101514 equals the main diagonal of A101515 shift one place right, and also A101514 shifts one place left under the square binomial transform (A008459): A101514(n+1) = Sum_{k=0..n-1} C(n-1,k)^2*A101514(k).
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FORMULA
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G.f.: A(x) = G101514(x^2/(1-x)^2)/(1-x)^2, where G101514(x)= g.f. of A101514. a(n) = Sum_{k=0..n} C(n, k)*A101514([k/2]).
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EXAMPLE
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Given A101514 = [1,1,2,7,35,236,2037,21695,277966,4198635,...],
the binomial transform of A101514 terms repeated twice returns this sequence:
BINOMIAL[1,1,1,1,2,2,7,7,35,35,...] = [1,2,4,8,17,38,91,232,632,1824,...].
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PROGRAM
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(PARI) {a(n)=sum(k=0, n, binomial(n, k)* if(k\2==0, 1, sum(j=0, k\2-1, binomial(k\2-1, j)^2* sum(i=0, 2*j, (-1)^(2*j-i)*binomial(2*j, i)*a(i)))))}
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CROSSREFS
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Cf. A101514, A101515.
Sequence in context: A086615 A081124 A090901 this_sequence A118928 A049312 A132043
Adjacent sequences: A101513 A101514 A101515 this_sequence A101517 A101518 A101519
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Dec 06 2004
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