The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A249268 Triangle read by rows: T(n,k) is the coefficient A_k in the transformation Sum_{k=0..n} x^k = Sum_{k=0..n} A_k*(x+3*(-1)^k)^k. 0
 1, 4, 1, -23, -5, 1, -320, -86, 10, 1, 4297, 1102, -152, -11, 1, 92020, 24187, -3122, -281, 16, 1, -1922207, -502151, 66133, 5659, -389, -17, 1, -55746464, -14601740, 1908316, 167254, -10784, -584, 22, 1, 1589338993, 415992316, -54490040, -4745234, 312406, 16048, -734, -23, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Consider the transformation 1 + x + x^2 + x^3 + ... + x^n = A_0*(x+3)^0 + A_1*(x-3)^1 + A_2*(x+3)^2 + A_3*(x-3)^3 + ... + A_n*(x+3*(-1)^n)^n. This sequence gives A_0, ... A_n as the entries in the n-th row of this triangle, starting at n = 0. LINKS EXAMPLE Triangle starts: 1; 4,                  1; -23,               -5,         1; -320,             -86,        10,        1; 4297,            1102,      -152,      -11,      1; 92020,          24187,     -3122,     -281,     16,     1; -1922207,     -502151,     66133,     5659,   -389,   -17,    1; -55746464,  -14601740,   1908316,   167254, -10784,  -584,   22,   1; 1589338993, 415992316, -54490040, -4745234, 312406, 16048, -734, -23, 1; ... PROG (PARI) a(n, j, L)=if(j==n, return(1)); if(j!=n, return(1-sum(i=1, n-j, (-L)^i*(-1)^(i*j)*binomial(i+j, i)*a(n, i+j, L)))) for(n=0, 10, for(j=0, n, print1(a(n, j, 3), ", "))) CROSSREFS Cf. A248975, A248977, A248811. Sequence in context: A243663 A039812 A308559 * A057869 A166027 A158978 Adjacent sequences:  A249265 A249266 A249267 * A249269 A249270 A249271 KEYWORD sign,tabl AUTHOR Derek Orr, Oct 23 2014 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 August 10 12:39 EDT 2020. Contains 336379 sequences. (Running on oeis4.)