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A256895 Triangle read by rows, T(n,k) = Sum_{j=0..n-k+1} j!*C(n-1,j-1)*T(n-j,k-1) if k != 0 else 1, n>=0, 0<=k<=n. 1
1, 1, 1, 1, 3, 1, 1, 11, 7, 1, 1, 49, 47, 13, 1, 1, 261, 341, 139, 21, 1, 1, 1631, 2731, 1471, 329, 31, 1, 1, 11743, 24173, 16213, 4789, 671, 43, 1, 1, 95901, 235463, 189373, 69441, 12881, 1231, 57, 1, 1, 876809, 2509621, 2357503, 1032245, 237961, 30169, 2087, 73, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Can be understood as a convolution matrix or as a sequence-to-triangle transformation similar to the partial Bell polynomials defined as: S -> T(n, k, S) = Sum_{j=0..n-k+1} C(n-1,j-1)*S(j)*T(n-j,k-1,S) if k != 0 else S(0)^n. Here S(n) = n!. The case S(n) = n gives the triangle of idempotent numbers A059297 and the case S(n) = 1 for all n leads to A256894.

LINKS

Table of n, a(n) for n=0..54.

FORMULA

T(n+1,1) = A001339(n) for n>=0.

T(n,n-1) = A002061(n) for n>=1.

EXAMPLE

Triangle starts:

1;

1, 1;

1, 3, 1;

1, 11, 7, 1;

1, 49, 47, 13, 1;

1, 261, 341, 139, 21, 1;

MAPLE

# Implemented as a sequence transformation acting on f: n -> n!.

F := proc(n, k, f) option remember; `if`(k=0, f(0)^n,

add(binomial(n-1, j-1)*f(j)*F(n-j, k-1, f), j=0..n-k+1)) end:

for n from 0 to 7 do seq(F(n, k, j->j!), k=0..n) od;

CROSSREFS

Cf. A001339, A002061, A059297, A256894.

Sequence in context: A113711 A257894 A103997 * A223256 A013561 A176468

Adjacent sequences:  A256892 A256893 A256894 * A256896 A256897 A256898

KEYWORD

nonn,tabl,easy

AUTHOR

Peter Luschny, Apr 28 2015

STATUS

approved

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Last modified November 12 09:29 EST 2019. Contains 329054 sequences. (Running on oeis4.)