This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A114202 A Pascal-Jacobsthal triangle. 4
 1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 8, 4, 1, 1, 5, 16, 16, 5, 1, 1, 6, 27, 42, 27, 6, 1, 1, 7, 41, 87, 87, 41, 7, 1, 1, 8, 58, 156, 216, 156, 58, 8, 1, 1, 9, 78, 254, 456, 456, 254, 78, 9, 1, 1, 10, 101, 386, 860, 1122, 860, 386, 101, 10, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Row sums are A114203. T(2n,n) is A114204. Inverse has row sums 0^n. LINKS Paul Barry, On Integer-Sequence-Based Constructions of Generalized Pascal Triangles, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.4. FORMULA As a number triangle, with J(n) = A001045(n): T(n, k) = Sum_{i=0..n-k} C(n-k, i)*C(k, i)*J(i); T(n, k) = Sum_{i=0..n} C(n-k, n-i)*C(k, i-k)*J(i-k); T(n, k) = Sum_{i=0..n} C(k, i)*C(n-k, n-i)*J(k-i) if k <= n, and 0 otherwise. As a square array, with J(n) = A001045(n): T(n, k) = Sum_{i=0..n} C(n, i)C(k, i)*J(i); T(n, k) = Sum_{i=0..n+k} C(n, n+k-i)*C(k, i-k)*J(i-k); Column k has g.f. (Sum_{i=0..k} C(k, i)*J(i+1)*(x/(1 - x))^i)*x^k/(1 - x). EXAMPLE Triangle begins   1;   1, 1;   1, 2,  1;   1, 3,  3,  1;   1, 4,  8,  4,  1;   1, 5, 16, 16,  5,  1;   1, 6, 27, 42, 27,  6, 1;   1, 7, 41, 87, 87, 41, 7, 1;   ... CROSSREFS Sequence in context: A073134 A300260 A026692 * A125806 A202756 A156354 Adjacent sequences:  A114199 A114200 A114201 * A114203 A114204 A114205 KEYWORD easy,nonn,tabl AUTHOR Paul Barry, Nov 16 2005 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified October 14 00:10 EDT 2019. Contains 327990 sequences. (Running on oeis4.)