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A084783 Triangle, read by rows, such that the diagonal (A084785) is the self-convolution of the first column (A084784) and the row sums (A084786) gives the differences of the diagonal and the first column. 4
1, 1, 2, 2, 3, 5, 6, 8, 11, 16, 25, 31, 39, 50, 66, 137, 162, 193, 232, 282, 348, 944, 1081, 1243, 1436, 1668, 1950, 2298, 7884, 8828, 9909, 11152, 12588, 14256, 16206, 18504, 77514, 85398, 94226, 104135, 115287, 127875, 142131, 158337, 176841, 877002 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Paul D. Hanna, Table of rows n=0..45, flattened.

FORMULA

T(0, 0)=1, T(n, 0)=A084784(n), T(k, k)=A084785(k), T(n, k)=T(n, k-1)+T(n-1, k-1) for n>0, k>0.

EXAMPLE

Triangle begins:

1;

1, 2;

2, 3, 5;

6, 8, 11, 16;

25, 31, 39, 50, 66;

137, 162, 193, 232, 282, 348;

944, 1081, 1243, 1436, 1668, 1950, 2298;

7884, 8828, 9909, 11152, 12588, 14256, 16206, 18504;

77514, 85398, 94226, 104135, 115287, 127875, 142131, 158337, 176841;

877002, 954516, 1039914, 1134140, 1238275, 1353562, 1481437, 1623568, 1781905; 1958746;

11218428, 12095430, 13049946, 14089860, 15224000, 16462275, 17815837, 19297274, 20920842, 22702747, 24661493; ...

PROG

(PARI) {A084784(n) = local(A); if( n<0, 0, A=1; for(k=1, n, A = truncate(A + O(x^k)) + x * O(x^k); A += A - 1 / subst(A^-2, x, x /(1 + x)) / (1 + x); ); polcoeff(A, n))}; /* After Michael Somos */

{T(n, k)=if(k==0, if(n==0, 1, A084784(n)), T(n, k-1)+T(n-1, k-1))}

for(n=0, 10, for(k=0, n, print1(T(n, k), ", ")); print(""))

CROSSREFS

Cf. A084784, A084785, A084786.

Sequence in context: A278298 A178927 A076571 * A265853 A129838 A032153

Adjacent sequences:  A084780 A084781 A084782 * A084784 A084785 A084786

KEYWORD

nonn,tabl

AUTHOR

Paul D. Hanna, Jun 13 2003

STATUS

approved

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Last modified July 14 09:22 EDT 2020. Contains 335720 sequences. (Running on oeis4.)