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A152037 Convolution of A007318 (Pascal's sequence) with itself . 3
1, 2, 3, 4, 7, 8, 9, 14, 20, 20, 21, 32, 43, 46, 51, 62, 71, 82, 107, 136, 145, 136, 144, 200, 280, 316, 296, 294, 359, 456, 535, 576, 591, 650, 820, 1020, 1078, 990, 963, 1160, 1541, 1950, 2225, 2244, 2034, 1892, 2211, 3024, 3866, 4260, 4207, 4066, 4150, 4630, 5617 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Paul D. Hanna, Table of n, a(n) for n = 0..1035

FORMULA

G.f.: [Sum_{n>=0} x^(n*(n+1)/2) * (1+x)^n ]^2. [From Paul D. Hanna, Apr 18 2012]

G.f.: [Sum_{n>=0} (1+x)^n*x^n * Product_{k=1..n} (1 - (1+x)*x^(2*k-1)) / (1 - (1+x)*x^(2*k)) ]^2. [From Paul D. Hanna, Apr 18 2012]

PROG

(PARI) {a(n)=local(A=sum(m=0, (sqrt(8*n+1)+1)\2, x^(m*(m+1)/2)*(1+x+x*O(x^n))^m)); polcoeff(A^2, n)} /* Paul D. Hanna, Apr 18 2012 */

for(n=0, 66, print1(a(n), ", "))

CROSSREFS

Cf. A182152, A182153, A007318.

Sequence in context: A321699 A050271 A322742 * A058075 A243495 A029783

Adjacent sequences:  A152034 A152035 A152036 * A152038 A152039 A152040

KEYWORD

nonn

AUTHOR

Philippe Deléham, Nov 20 2008

EXTENSIONS

More terms (and corrected term) from L. Edson Jeffery, Apr 23, 2011.

STATUS

approved

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Last modified January 20 14:13 EST 2019. Contains 319333 sequences. (Running on oeis4.)