A101516 Antidiagonal sums of symmetric square array A101515 and also equals the binomial transform of a sequence formed from terms of A101514 repeated twice.

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

Offset

0,2

Comments

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).

Links

Table of n, a(n) for n=0..26.

Formula

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]).

Example

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,...].

Prog

(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)))))}

Crossrefs

Cf. A101514, A101515.

Sequence in context: A081124 A340776 A090901 * A118928 A325921 A049312

Adjacent sequences: A101513 A101514 A101515 * A101517 A101518 A101519

Keyword

nonn

Author

Paul D. Hanna, Dec 06 2004

Status

approved