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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

Paul D. Hanna, Table of n, a(n), n = 1..496 (rows 1..31).

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:

T*A158831 = A158832; T*A158832 = A158833; T*A158833 = A158834;

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.

Cf. A158825, A158831, A158832, A158833, A158834, variant: A135080.

Sequence in context: A239894 A152406 A105623 * A236961 A245958 A138271

Adjacent sequences:  A158832 A158833 A158834 * A158836 A158837 A158838

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 January 22 07:39 EST 2020. Contains 331139 sequences. (Running on oeis4.)