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A158835 Triangle, read by rows, that transforms diagonals in the array A158825 of coefficients of successive iterations of x*C(x) where C(x) is the Catalan function (A000108). 12
1, 1, 1, 4, 2, 1, 27, 11, 3, 1, 254, 94, 21, 4, 1, 3062, 1072, 217, 34, 5, 1, 45052, 15212, 2904, 412, 50, 6, 1, 783151, 257777, 47337, 6325, 695, 69, 7, 1, 15712342, 5074738, 906557, 116372, 12035, 1082, 91, 8, 1, 357459042, 113775490, 19910808, 2483706 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,4
LINKS
EXAMPLE
Triangle T begins:
1;
1,1;
4,2,1;
27,11,3,1;
254,94,21,4,1;
3062,1072,217,34,5,1;
45052,15212,2904,412,50,6,1;
783151,257777,47337,6325,695,69,7,1;
15712342,5074738,906557,116372,12035,1082,91,8,1;
357459042,113775490,19910808,2483706,246596,20859,1589,116,9,1;
9094926988,2861365660,492818850,60168736,5801510,470928,33747,2232,144,10,1;
...
Array A158825 of coefficients in iterations of x*C(x) begins:
1,1,2,5,14,42,132,429,1430,4862,16796,58786,208012,742900,...;
1,2,6,21,80,322,1348,5814,25674,115566,528528,2449746,...;
1,3,12,54,260,1310,6824,36478,199094,1105478,6227712,...;
1,4,20,110,640,3870,24084,153306,993978,6544242,43652340,...;
1,5,30,195,1330,9380,67844,500619,3755156,28558484,...;
1,6,42,315,2464,19852,163576,1372196,11682348,100707972,...;
1,7,56,476,4200,38052,351792,3305484,31478628,303208212,...;
1,8,72,684,6720,67620,693048,7209036,75915708,807845676,...;
1,9,90,945,10230,113190,1273668,14528217,167607066,...;
1,10,110,1265,14960,180510,2212188,27454218,344320262,...;
...
This triangle transforms diagonals of A158825 into each other:
where:
A158831 = [1,1,6,54,640,9380,163576,3305484,...];
A158832 = [1,2,12,110,1330,19852,351792,7209036,...];
A158833 = [1,3,20,195,2464,38052,693048,14528217,...];
A158834 = [1,4,30,315,4200,67620,1273668,27454218,...].
PROG
(PARI) {T(n, k)=local(F=x, CAT=serreverse(x-x^2+x*O(x^(n+2))), M, N, P, m=max(n, k)); M=matrix(m+2, m+2, r, c, F=x; for(i=1, r+c-2, F=subst(F, x, CAT)); polcoeff(F, c)); N=matrix(m+1, m+1, r, c, M[r, c]); P=matrix(m+1, m+1, r, c, M[r+1, c]); (P~*N~^-1)[n+1, k+1]}
for(n=0, 12, for(k=0, n, print1(T(n, k), ", ")); print(""))
CROSSREFS
Cf. columns: A158836, A158837, A158838, A158839, row sums: A158840.
Sequence in context: A152406 A105623 A364870 * A236961 A245958 A138271
KEYWORD
nonn,tabl
AUTHOR
Paul D. Hanna, Mar 28 2009, Mar 29 2009
EXTENSIONS
Edited by N. J. A. Sloane, Oct 04 2010, to make entries, offset, b-file and link to b-file all consistent.
STATUS
approved

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Last modified March 29 11:45 EDT 2024. Contains 371278 sequences. (Running on oeis4.)