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A095675 Triangle read by rows, formed from product of Aitken's (or Bell's) triangle (A011971) and Pascal's triangle (A007318). 2

%I

%S 1,3,2,10,13,5,37,72,55,15,151,393,450,245,52,674,2202,3365,2748,1166,

%T 203,3263,12850,24582,26781,17048,5936,877,17007,78488,180477,245971,

%U 208856,109107,32243,4140,94828,502327,1349900,2209695,2346559,1634998

%N Triangle read by rows, formed from product of Aitken's (or Bell's) triangle (A011971) and Pascal's triangle (A007318).

%C These triangles are to be thought of as infinite lower-triangular matrices.

%e Triangle begins:

%e 1

%e 3 2

%e 10 13 5

%e 37 72 55 15

%e 151 393 450 245 52

%t a[0, 0] = 1; a[n_, 0] := a[n - 1, n - 1]; a[n_, k_] := a[n, k] = If[k < n + 1, a[n, k - 1] + a[n - 1, k - 1], 0]; p[n_, r_] := If[r <= n + 1, Binomial[n, r], 0]; am = Table[ a[n, r], {n, 0, 9}, {r, 0, 9}]; pm = Table[p[n, r], {n, 0, 9}, {r, 0, 9}]; t = Flatten[am.pm]; Delete[ t, Position[t, 0]] (* _Robert G. Wilson v_, Jul 12 2004 *)

%Y Cf. A007318, A011971, A095674. Row sums give A095676. First column is A005493.

%K nonn,tabl,easy

%O 0,2

%A _N. J. A. Sloane_, based on a suggestion from _Gary W. Adamson_, Jun 22 2004

%E More terms from _Robert G. Wilson v_, Jul 13 2004

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Last modified May 24 09:41 EDT 2019. Contains 323529 sequences. (Running on oeis4.)