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A257566 Triangle read by rows, T(n,k) = Sum_{j=0..n-k+1} P(n,j)*T(n-j,k-1) if k>0 else 0^n where P(n,j) is the number of j-partitions of n; for n>=0 and 0<=k<=n. 1
1, 0, 1, 0, 2, 1, 0, 3, 4, 1, 0, 5, 13, 7, 1, 0, 7, 30, 30, 10, 1, 0, 11, 76, 119, 65, 14, 1, 0, 15, 152, 357, 306, 113, 18, 1, 0, 22, 330, 1119, 1375, 746, 193, 23, 1, 0, 30, 633, 2973, 5059, 3888, 1497, 295, 28, 1, 0, 42, 1245, 8036, 18605, 19423, 10298, 2930, 447, 34, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Table of n, a(n) for n=0..65.

FORMULA

T(n,1) = A000041(n) for n>=1.

T(n,n-1) = A014616(n-1) for n>=2.

EXAMPLE

1;

0,  1;

0,  2,  1;

0,  3,  4,   1;

0,  5, 13,   7,  1;

0,  7, 30,  30, 10,  1;

0, 11, 76, 119, 65, 14, 1;

MAPLE

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

add(combinat:-numbpart(n, j)*T(n-j, k-1), j=0..n-k+1)) end:

for n from 0 to 12 do seq(T(n, k), k=0..n) od;

CROSSREFS

Cf. A000041, A014616.

Sequence in context: A300454 A155112 A256130 * A188286 A101603 A228161

Adjacent sequences:  A257563 A257564 A257565 * A257567 A257568 A257569

KEYWORD

nonn,tabl,easy

AUTHOR

Peter Luschny, Apr 30 2015

STATUS

approved

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Last modified April 22 14:52 EDT 2019. Contains 322356 sequences. (Running on oeis4.)