A102472 Triangle read by rows. Let S(k) be the sequence defined by F(0)=0, F(1)=1, F(n-1) + (n+k)*F(n) = F(n+1). E.g. S(0) = 0, 1, 1, 3, 10, 43, 225, 1393, 9976, 81201, ... Then S(0), S(1), S(2), ... are written vertically, next to each other, with the initial term of each on the next row down.

1, 1, 1, 3, 2, 1, 10, 7, 3, 1, 43, 30, 13, 4, 1, 225, 157, 68, 21, 5, 1, 1393, 972, 421, 130, 31, 6, 1, 9976, 6961, 3015, 931, 222, 43, 7, 1, 81201, 56660, 24541, 7578, 1807, 350, 57, 8, 1, 740785, 516901, 223884, 69133, 16485, 3193, 520, 73, 9, 1

Offset

1,4

Comments

T(n,1) = A001040(n); T(n,k) = A058294(n,n+k-1), k = 1..n. - Reinhard Zumkeller, Sep 14 2014

This triangle results when the first column is removed from A062323. - Georg Fischer, Jul 26 2023

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..7875

Example

Triangle begins:
[1] 1;
[2] 1, 1;
[3] 3, 2, 1;
[4] 10, 7, 3, 1;
[5] 43, 30, 13, 4, 1;
[6] 225, 157, 68, 21, 5, 1;
[7] 1393, 972, 421, 130, 31, 6, 1;
[8] 9976, 6961, 3015, 931, 222, 43, 7, 1;

Prog

(Haskell)
a102472 n k = a102472_tabl !! (n-1) !! (k-1)
a102472_row n = a102472_tabl !! (n-1)
a102472_tabl = map reverse a102473_tabl
-- Reinhard Zumkeller, Sep 14 2014

Crossrefs

Mirror image of triangle in A102473.

Cf. A001040, A058294, A062323, A247365 (central terms).

Sequence in context: A307214 A185967 A188111 * A267629 A101894 A187105

Adjacent sequences: A102469 A102470 A102471 * A102473 A102474 A102475

Keyword

easy,nonn,tabl

Author

Russell Walsmith, Jan 09 2005

Extensions

Entry revised by N. J. A. Sloane, Jul 09 2005

Status

approved